4th - Kırşehir Ahi Evran University€¦ · It was a great moment of excitement when Prof. (Dr.) Vatan Karakaya, Rector, Ahi Evran University, discussed with me the matter of organizing

4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr

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4th INTERNATIONAL CONFERENCE ON ANALYSIS

AND ITS APPLICATIONS

SEPTEMBER 11-14, 2018, KIRSEHIR / TURKEY

Abstract Book

Editors

Prof.Dr. Vatan KARAKAYA

Rector of Kırşehir Ahi Evran University

Kırşehir, TURKEY

Prof.Dr. Mohammad MURSALEEN

Aligarh Muslim University

Aligarh, INDIA

Prof. Dr. Necip ŞİMŞEK

İstanbul Commerce University

İstanbul, TURKEY

Prof.Dr. Qamrul Hasan ANSARI

Aligarh Muslim University

Aligarh, INDIA

ISBN : 978-605-85712-8-0

Kırşehir Ahi Evran University, Kırşehir / TURKEY - 2018

http://websiteyonetimi.ahievran.edu.tr/_Dosyalar/Genel/8bf368fe-87d8-49f6-af18-4aa29d3ad5b4-9f763441-54c9-4597-a1bb-3f5477ba3df9.pdf

http://www.amu.ac.in/dshowfacultydata.jsp?did=6&eid=605

http://ww3.ticaret.edu.tr/nsimsek/

http://www.amu.ac.in/dshowfacultydata.jsp?did=6&eid=601


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FOREWORDS

Dear Conference Participants,

First of all, I would like to thank you for coming today to participate at this opening ceremony and I wish

to welcome you to Turkey and Kırşehir. I hope we will have a good time during this conference.

Kırşehir Ahi Evran University was founded on March 17, 2006 in Kırşehir which is located in the center

of Turkey. With approximately 22 thousand students and more than 800 academicians, our university is

a young and dynamic university. Our university consists of 39 academic units, including 8 faculties, 3

institutions, 5 schools of higher education, 7 vocational schools of higher education and 16 research

and application centers, and 7 different campuses in which education maintains.

Kırşehir Ahi Evran University, by the President of the Republic of Turkey Mr. Recep Tayyip Erdogan

made a statement on 18.01.2016, is selected as one of five pilot universities in the field of agriculture

and geothermal by within the scope of “Regional Development Focused Mission Differentiation and

Specialization Project”. Ahi Evran University is also the first and only university to be awarded the ISO

9001: 2015 Quality Management System Certificate by successfully completing the ISO 9001: 2015

Quality Management Standard External Audit Process with all its units.

The projects of our university are

• Geothermal Welding and Transmission to Project Fields

• Clustering Project in Thermal Sera

• Roughage Production Project

• Walnut-Focused Development and Development Project

• Geothermal Rehabilitation Center Project

• Sportsman Health Research, Application and Thermal Rehabilitation Center Project

• Training and Promotion Project of Pilot University Projects.

I would like to share some historical information about Kırşehir. Kırşehir is a region with a number of

prominent cultures which have lived throughout the history and it has the traces of Hititian, Phrygian,

Lydian, Cappadocian, Roman, Seldjukian and Ottoman civilizations. Also it is the homeland of Aşıkpaşa

who wrote the first Turkish masterpiece, Cacabey who carried out astronomical studies by examining

the stars reflecting on water inside a well in the madrasa he founded, Ahi Evran-ı Veli who organized

merchants and craftsmen, Yunus Emre, Ahmet Gülşehri, Süleyman Türkmani, Şeyh Edabali and Mesut

Gülşehri who contributed in literature and culture.

The fundamental duty of universities is to produce information. The means of these are conferences,

symposiums, workshops, etc. In this sense, we will discuss problems related to mathematics and reach

to solutions in this conference.

The purpose of this conference is to bring together experts and young analysts from all over the world

working in different fields of mathematics and its applications to present their researches, exchange new

ideas, discuss challenging issues, foster future collaborations and interact with each other.


4

This conference allows the participation of many prominent experts from different countries who will

present works on different fields of mathematics, especially fixed point theory, approximation theory,

nonlinear analysis, variational analysis, optimization, summability theory, sequence spaces, dynamical

systems and their applications, and also algebra, geometry.

It bring together more than 130 participants from countries of different part of the world for example

Algeria, Ajarian, Azerbaijan, Egypt, Congo, Yemen, Korea, China, India, Iran, Sudan, Morocco, Saudi

Arabia, Tunisia, Ghana, Turkey, Uzbekistan, United States of America, Jordan, out of which 124 are

contributing to the meeting with oral and 3 with poster presentations, including five plenary talks.

We also thank pleanery speaker distinguished Prof. Mohammad MURSALEEN, distinguished Prof.

Zuhair NASHED, distinguished Prof. Jong Kyu KIM, distinguished Prof. Qamrul Hasan ANSARI and

distinguished Prof. Bayram ŞAHİN for contribution to the our symposium.

We hope to promote collaborative and networking opportunities among senior scholars and graduate

students in order to advance new perspectives. The additional emphasis at ICAA-2018 is to put

importance on applications in related areas, as well as other science, such as natural science,

economics, computer science and various engineering sciences.

The papers presented in this conference will be considered in the journals listed on the conference

websites and below:

• Journal of Nonlinear and Convex Analysis (SCI-Exp),

• Carpathian Journal of Mathematics (SCI-Exp),

• Bulletin of Mathematical Analysis and Applications (E-SCI),

• Journal of Inequalities and Special Functions (E-SCI.),

• Creative Mathematics and Informatics,

• Istanbul Commerce University Journal of Science,

• Nonlinear Functional Analysis and Applications (SCOPUS).

This booklet contains the titles and abstracts of almost all invited and contributed talks at the 4th

International Conference on Analysis and Its Applications. Only some abstracts were not available

at the time of printing the booklet. They will be made available on the conference website

www.icaa2018.org when the organizers receive them. All talks will take place in Faculty of Arts and

Sciences in Ahi Evran University, Bağbaşı Campus, Kırşehir/Turkey.

We wish everyone a fruitful conference and pleasant memories in Kırşehir, Turkey.

Prof. Vatan KARAKAYA

On Behalf of Organizing Committee

Chairman

(Rector of Ahi Evran University)

http://www.ybook.co.jp/jnca.html

http://carpathian.ubm.ro/

http://www.ybook.co.jp/jnca.html

http://www.journalofinequalitiesandapplications.com/

http://creative-mathematics.ubm.ro/

http://dergipark.ulakbim.gov.tr/ticaretfbd/

http://www.icaa2018.org/


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Analysis is one of the most important topics in mathematics and has been a focus of attention

of all great mathematicians. There are many areas comes under this topic. However, this conference

mainly devoted to some selected topics from analysis, mainly, Theory of Summability and

Approximation, Fixed Point Theory, Fourier Analysis, Wavelet and Harmonic Analysis, Variational

Analysis, Convex Analysis and Optimization, Geometry of Banach Spaces, Sequence Spaces and

Matrix Transformations. During the last half century, nonlinear and variational analysis have been

developed very rapidly because of their numerous applications to optimization, control theory,

economics, engineering, management, medical sciences and other disciplines. On the other hand, the

modern summability theory plays a very important role in linking theory of sequence spaces and matrix

transformations with measures of noncompactness. Measures of noncompactness are widely used tools

in fixed point theory, differential equations, functional equations, integral and integro-differential

equations, optimization, etc. In the recent years, measures of noncompactness have also been used in

defining geometric properties of Banach spaces as well as in characterizing compact operators between

sequence spaces. We expect the participation of many prominent experts from different countries who

will present their current research work and will also mention some hot topics for further research.

Prof. Qamrul Hasan ANSARI

It was a great moment of excitement when Prof. (Dr.) Vatan Karakaya, Rector, Ahi Evran

University, discussed with me the matter of organizing the “International Conference on Analysis and Its

Applications (ICAA-2018)” at Ahi Evran University, Kırşehir. Now it is a matter of great pleasure that the

matter of holding this conference is finally materialized. This conference is in the sequel of the first one

which was held during December 19-21, 2015 (ICAA-2015) in Aligarh Muslim University, India, the

second one which was held during July12-15, 2016 (ICAA-2016) in Ahi Evran University, Kırşehir and

third one was held during November 20-22, 2017 (ICAA-2017) in Aligarh Muslim University. Being one

of the Co-Chairmen of the conference, I feel privileged and delighted to welcome all delegates, eminent

mathematicians, speakers and young researchers in this international event. It is expected that the

delegates and the participants will be benefitted by the experience of this conference and the legacy of

knowledge dissemination will be continued.I wish all of you to have a nice and enjoyable participation in

the conference. Prof. Mohammad MURSALEEN

We are deeply honored to be the host of this prestigious International Conference on Analysis

and Its Applications (ICAA-2018). On behalf of organizing committee, I would like to extend my heartiest

welcome to all the invited speakers, presenters and participants and to thank all of you for your

support.At this conference we had the opportunity to meet and host many valuable scientists from

different countries of the world. We have received more than 120 papers for presenting. Corresponding

participants have joined us in presenting their ideas and achievements, as well as participated in the

International Conference on Analysis and Its Applications (ICAA-2018)”. We hope that, this conference

will promote the sharing of experiences and strengthen collaborations among the participants doing and

applying mathematics. My deepest appreciation goes for his valuable support in organizing the

conference to Prof. KARAKAYA, who is the Chairman of the ICAA-2018 and Rector of the Kırşehir Ahi

Evran University. Also, I would like to thank the honorable scientists Prof. Ansari, Prof. Kim, Prof.

Mursaleen, Prof. Nashed and Prof. Şahin for accepting our invitation to join the conference as a invited

speaker. Finally, I would like to thank the presenters, participants, the ICAA-2018 working committee for

their hard work and decisiveness, and any who have directly or indirectly contributed to make ICAA-

2018 a success.

Prof. Necip ŞİMŞEK


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Scientific Committee

A. Ioan RUS (Romania) Manaf MANAFLI (Turkey)

Abdul Rahim KHAN (Saudi Arabia) Mehmet Ali SARIGÖL (Turkey)

Akhtam DZHALİLOV (Uzbekistan) Mehmet Emin ÖZDEMİR (Turkey)

Aldona DUTKIEWICZ (Poland) Metin BAŞARIR (Turkey)

Ali AKBULUT (Turkey) Mikail ET (Turkey)

Ayhan ŞERBETÇİ (Turkey) Mohamed Amine KHAMSI (USA)

Bayram ŞAHİN (Turkey) Mohammad MURSALEEN (India)

Billy E. RHOADES (USA) Mohammad IMDAD (India)

Brailey SIMS (Australia) Murat KİRİŞÇİ (Turkey)

Bünyamin AYDIN (Turkey) Murat ÖZDEMİR (Turkey)

Calogero VETRO (Italy) Murat SARI (Turkey)

Cemil TUNÇ (Turkey) Müzeyyen ERTÜRK (Turkey)

Davide LA TORRE (UAE, Italy) Naim L. BRAHA (Kosova)

Daya Ram SAHU (India) Narin PETROT (Thailand)

Doğan KAYA (Turkey) Nazim B. KERİMOV (Turkey)

Duran TÜRKOĞLU (Turkey) Necip ŞİMŞEK (Turkey)

Ekrem SAVAŞ (Turkey) Nour El Houda BOUZARA (Algeria)

Emrah Evren KARA (Turkey) P. VEERAMANI (India)

Fahreddin ABDULLAYEV (Turkey) Poom KUMAM (Thailand)

Faik GÜRSOY (Turkey) Pratulananda DAS (India)

Fatih NURAY (Turkey) QamrulHasan ANSARI (India)

Franco GIANNESSI (Italy) Rais AHMAD (India)

Gradimir V. MILOVANOVIC (Serbia) Ravi P. AGARWAL (USA)

Hamdullah ŞEVLİ (Turkey) Rıfat ÇOLAK (Turkey)

Hanlar REŞİDOĞLU (Turkey) Richard F. PATTERSON (USA)

Harun POLAT (Turkey) Sebaheddin ŞEVGİN (Turkey)

Henryk HUDZIK (Poland) Seyit TEMİR (Turkey)

Heybetkulu S MUSTAFAYEV (Turkey) Sezgin AKBULUT (Turkey)

Hong-Kun XU (China) Suheil A. KHOURY (UAE)

Hüseyin ÇAKALLI (Turkey) Ştefan MARUŞTER (Romania)

İlham ALİYEV (Turkey) Themistocles M. RASSIAS (Greece)

İsmail EKİNCİOĞLU (Turkey) Tomás Domínguez BENAVIDES (Spain)

İsmail KÜÇÜK (Turkey) Vagif GULİYEV (Azerbaijan)

Jen-Chih YAO (Taiwan) Vasile BERINDE (Romania)

Jesús Garcia-FALSET (Spain) Viktor I. BURENKOV (England)

Johannes J. A. EKSTEEN (South Africa) Vishnu Narayan MISHRA (India)

Johnson O. OLALERU (Nigeria) W.C. WONG (Taiwan)

Jong Kyu KIM ( Korea) Wataru TAKAHASHI (Japan)

Józef BANAS (Poland) William Art KIRK (USA)

Kadri DOĞAN (Turkey) Yılmaz ALTUN (Turkey)

Kaleem Raza KAZMI (India) Yunus ATALAN (Turkey)

Kazimierz GOEBEL (Poland) Zuhair NASHED (USA)


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Organizing Committee

Prof. Dr. Vatan KARAKAYA, Chairman, Yildiz Technical University, Istanbul, Turkey

Prof. Dr. Mohammad MURSALEEN, Co-Chair, Aligarh Muslim University, Aligarh, India

Prof. Dr. Necip ŞİMŞEK, Co-Chair, Istanbul Commerce University, Turkey

Prof. Dr. Qamrul Hasan ANSARI, Co-Chair, Aligarh Muslim University, Aligarh, India

Assoc. Prof. Dr. Faik GÜRSOY, Adıyaman University, Adıyaman, Turkey

Assoc. Prof. Dr. Handan KÖSE, Ahi Evran University, Kirsehir, Turkey

Assoc. Prof. Dr. Müzeyyen ERTÜRK, Adıyaman University, Adıyaman, Turkey

Assist. Prof. Dr. Javid ALI, Aligarh Muslim University, Aligarh, India

Assist. Prof. Dr. Kadri DOĞAN, Artvin Çoruh University, Artvin, Turkey

Assist. Prof. Dr. Nil MANSUROĞLU, Ahi Evran University, Kirsehir, Turkey

Assist. Prof. Nour El Houda BOUZARA, University of Sci. and Tech., Algeria

Assist. Prof. Dr. Yunus ATALAN, Aksaray University, Turkey

Res. Assist. Arife Aysun KARAASLAN, Işık University, Istanbul, Turkey

Res. Assist. Derya SEKMAN, Ahi Evran University, Kirsehir, Turkey

Res. Assist. Emirhan HACIOĞLU, Yildiz Technical University, Istanbul, Turkey

Phd. Stud. Muhammed KNEFATIi, Yildiz Technical University, Istanbul, Turkey

Msc. Stud. Zhamile ASKEROVA, Istanbul Commerce University, Turkey

Phd. Stud. Reyhan TELLİOĞLU, Istanbul Commerce University, Turkey

Phd. Stud. Ruken ÇELİK, Istanbul Commerce University, Turkey

TABLE OF CONTENTS

FOREWORDS .................................................................................................................................................... 3

SCIENTIFIC COMMITTEE ................................................................................................................................... 6

ORGANIZING COMMITTEE ................................................................................................................................ 7

PLENARY TALKS ............................................................................................................................................. 13

EKELAND’S VARIATIONAL PRINCIPLE FOR SET-VALUED MAPS........................................................................ 13

Qamrul Hasan ANSARI

SOME RESULTS ON A COMMON ZERO OF A FINITE FAMILY OF ACCRETIVE OPERATORS IN BANACH SPACES ... 14

Jong Kyu KIM

APPLICATIONS OF MEASURES OF NONCOMPACTNESS TO MATRIX TRANSFORMATIONS AND DIFFERENTIAL

AND INTEGRAL EQUATIONS ......................................................................................................................... 15

Mohammad MURSALEEN

PERTURBATION ANALYSIS FOR GENERALIZED INVERSES OF LINEAR OPERATORS AND THE ROLE OF OUTER

INVERSES IN REGULARIZATION OF ILL-POSED PROBLEMS.............................................................................. 16

Zuhair NASHED

RIEMANNIAN MAPS IN KAEHLER GEOMETRY ................................................................................................ 17

Bayram ŞAHİN

CONTRIBUTED TALKS ..................................................................................................................................... 18

ROOTS OF ANALYSIS IN ISLAMIC MATHEMATICS ........................................................................................... 18

Abdulmajid NUSAYR

WAVELET PACKET TRANSFORMATION ASSOCIATED WITH LINEAR CANONICAL HANKEL TRANSFORMATION .. 19

Akhilesh PRASAD, Tanuj KUMAR

CONVERGENCE THEOREMS FOR SOME MAPPINGS IN A TYPE OF PROBABILISTIC NORMED SPACES ................ 20

Arife Aysun KARAASLAN, Vatan KARAKAYA

ON GENERALIZED TRIBONACCI OCTONIONS ................................................................................................. 21

Arzu ÖZKOÇ ÖZTÜRK

SOME INVESTIGATIONS FOR TIME FRACTIONAL KORTEWEG-DE VRIES EQUATION USING THE FINITE

DIFFERENCE METHOD .................................................................................................................................. 22

Asıf YOKUS

SOME NEW RESULTS OF M-ITERATION PROCESS IN HYPERBOLIC SPACES ...................................................... 23

Aynur ŞAHİN

DG SOLUTION OF DIFFUSION-REACTION PROBLEM TO MODEL THE DENSITY OF TUMOR GROWTH DYNAMIC 24

Ayşe SARIAYDIN-FİLİBELİOĞLU

NOTES ON GENERATED Q-POLY GENOCCHI POLYNOMIALS ........................................................................... 25

Burak KURT

THINNESS AND FINE TOPOLOGY WITH RELATIVE CAPACITY ........................................................................... 26

Cihan UNAL, Ismail AYDIN

ON APPLICATIONS OF MULTIDIMENSIONAL AFFINE TRANSFORM IN THE SUPPLY OF MISSING DATA .............. 27

Cuneyt YAZICI, Suleyman CETINKAYA, Hulya KODAL SEVİNDİR

DIMENSION OF PRODUCT OF FOUR HOMOGENEOUS COMPONENTS IN FREE LIE ALGEBRAS .......................... 28

Derya KARATAŞ, Nil MANSUROĞLU

ON THE F-CONTRACTION OF THE DARBO THEOREM GENERALIZED BY FUNCTION CLASSES ............................ 29

Derya SEKMAN, Vatan KARAKAYA

ISHIKAWA ITERATION PROCESS AS CONTROL SYSTEMS AND CHAOTIC DISCRETE DYNAMICAL SYSTEMS ......... 30


9

Derya SEKMAN, Vatan KARAKAYA

SYMMETRY ANALYSIS AND CONSERVATION LAWS OF THE BOUNDARY VALUE PROBLEMS FOR TIME-

FRACTIONAL GENERALIZED BURGERS' DIFFERENTIAL EQUATION .................................................................. 31

Dogan KAYA, Gulistan ISKANDAROVA

SOME REMARKS RELATED TO CONTRACTION MAPPINGS ON F-METRIC SPACES ............................................ 32

Emrah Evren KARA, Merve İLKHAN

SOME NEW INEQUALITIES AND HERMITE-HADAMARD-FEJER INEQUALITY VIA NON-NEWTONIAN CALCULUS 33

Erdal ÜNLÜYOL, Yeter ERDAŞ

ASYMPTOTICALLY 𝑰𝟐-INVARIANT EQUIVALENCE OF DOUBLE SEQUENCES AND SOME PROPERTIES ................ 34

Erdinç DÜNDAR, Uğur ULUSU and Fatih NURAY

HELICOIDAL HYPERSURFACES OF DINI-TYPE IN THE FOUR DIMENSIONAL MINKOWSKI SPACE ........................ 35

Erhan GÜLER, Ömer KiŞi

TORUS HYPERSURFACE IN 4-SPACE .............................................................................................................. 36

Erhan GÜLER, Ömer KiŞi

ON QUASI-LACUNARY INVARIANT CONVERGENCE OF SEQUENCES OF SETS ................................................... 37

Esra GÜLLE, Uğur ULUSU

SOME FIXED POINT RESULTS FOR A NEW THREE STEPS ITERATION PROCESS IN BANACH SPACES: A REVISIT ... 38

Faik GÜRSOY, Müzeyyen ERTÜRK, Vatan KARAKAYA

AN APPLICATION OF THREE DIMENSIONAL CELLULAR AUTOMATA WITH PBC .............................................. 39

Ferhat SAH

AN APPLICATION OF ONE DIMENSIONAL CELLULAR AUTOMATA UNDER INTERMEDIATE BOUNDARY

CONDITION ................................................................................................................................................. 40

Ferhat SAH

NUMERICAL APPROACH BASED ON LAGRANGE POLYNOMIALS FOR SOLVING FREDHOLM INTEGRAL

EQUATIONS ................................................................................................................................................. 41

Fernane KHAIREDDINE

SOME BOUNDS OF THE FINITE HILBERT TRANSFORM AND APPLICATIONS IN NUMERICAL INTEGRATION ....... 42

Fuat USTA

P-3-PRIME IDEALS IN NEAR RINGS ................................................................................................................ 43

Funda TAŞDEMİR, İsmail TAŞTEKİN

ON INCLUSION THEOREMS FOR ABSOLUTE CESÀRO SUMMABILITY METHODS ............................................. 44

G. Canan HAZAR GÜLEÇ, M. Ali SARIGÖL

ON THE ZERO POINT PROBLEM OF MONOTONE OPERATORS IN CAT(0) SPACES ............................................. 45

G. Zamani ESKANDANI, M. RAEISI

ON MIZOGUCHI-TAKAHASHI'S TYPE SET VALUED (Α-Θ) CONTRACTIONS ......................................................... 46

Gonca DURMAZ, İshak ALTUN, Murat OLGUN ,Hatice ASLAN HANÇER

NOVEL CONTOUR SURFACES TO THE (2+1)-DIMENSIONAL DATE–JIMBO–KASHIWARA–MIWA EQUATION ..... 47

Haci Mehmet BASKONUS

ON THE ROOTS OF AN EVOLUTION EQUATION.............................................................................................. 48


SOME CARISTI TYPE FIXED POINT THEOREMS ON M-METRIC SPACE .............................................................. 49

Hakan SAHIN, İshak ALTUN, Duran TURKOGLU, Hatice ASLAN HANCER

QUASI-HAUSDORFF TRANSFORMATIONS FOR DOUBLE SEQUENCES ............................................................. 50

Hamdullah ŞEVLİ

WEIGHTED COMPOSITION OPERATORS FROM BLOCH-TYPE SPACES INTO BERS-TYPE SPACES ...................... 51

Hamid VAEZI, Mohamad NAGHLISAR

ON SEMICOMMUTATIVE RINGS ................................................................................................................... 52

Handan KOSE


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SOME OPERATOR INEQUALITIES .................................................................................................................. 53

Havva TİLKİ, Mualla Birgül HUBAN, Mehmet GÜRDAL

EPI EULER CONVERGENCE OF KIND CONVERGENT SETS ................................................................................ 54

Harun POLAT

NEW TOPOLOGY IN 𝜷(𝐼) .............................................................................................................................. 55

Hassan MOUADI, Driss KARIM

INVESTIGATION OF SUBORBİTAL GRAPHS OF THE TYPE Γ0(L, M) = (A BM

CL D) ........................................................ 56

İbrahim GÖKCAN

WEIGHTED STOCHASTIC FIELD EXPONENT LEBESGUE AND SOBOLEV SPACES ................................................ 57

Ismail AYDIN, Cihan UNAL

SOME COMPACTNESS CRITERIONS IN WEIGHTED VARIABLE EXPONENT AMALGAM SPACES .......................... 58

Ismail AYDIN, Cihan UNAL

CONVERGENCE ANALYSIS OF A NEW MODIFIED JUNGCK-THREE-STEP ITERATIVE METHOD IN THE BANACH

SPACES ........................................................................................................................................................ 59

Kadri DOĞAN, Yılmaz ALTUN

CONVERGENCE ANALYSIS OF JUNGCK-MP ITERATIVE METHOD IN THE BANACH SPACES ................................ 60

Kadri DOĞAN, Vatan KARAKAYA

FIXED POINT THEOREMS VIA SIMULATION TYPE FUNCTIONS ........................................................................ 61

Merve İLKHAN

Δ - CONVERGENCE AND STRONG CONVERGENCE IN GENERALIZED CAT (0) SPACES........................................ 62

Mohammad KNEFATI and Vatan KARAKAYA

ON I2-CAUCHY DOUBLE SEQUENCES IN FUZZY NORMED SPACE ..................................................................... 63

Muhammed Recai TÜRKMEN, Erdinç DÜNDAR

LACUNARY STATISTICAL CONVERGENCE IN FUZZY N-NORMED LINEAR SPACES .............................................. 64

Muhammed Recai TÜRKMEN

SOME RESULTS ON 𝝀 − STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES IN FUZZY NORMED SPACE ...... 65


LACUNARY I-CONVERGENCE IN FUZZY NORMED SPACES .............................................................................. 66


NEW TYPE SOFT SET AND MEDICAL DECION MAKING APPLICATION .............................................................. 67

Murat KİRİŞCİ

REASONABLE MODIFICATIONS UNDER THE B-SPLINE BASIS WITH THE SSPRK54 FOR SOLVING THE BURGERS

EQUATION................................................................................................................................................... 68

Murat SARI, S. Ali-TAHIR

NEW JUNGCK-TYPE ITERATIVE ALGORITHM AND NUMERICAL RECKONING COINCIDENCE POINTS IN CONVEX

METRIC SPACES ........................................................................................................................................... 69

Musa DİKMEN, Faik GÜRSOY

SOME FIXED POINT THEOREMS IN CONE METRIC SPACES OVER BANACH ALGEBRAS...................................... 70

Muttalip ÖZAVŞAR

ON FINITE DIMENSIONAL LEIBNIZ ALGEBRAS ................................................................................................ 71

Mücahit ÖZKAYA, Nil MANSUROĞLU

CONVERGENCE AND STABILITY RESULTS FOR K* ITERATION.......................................................................... 72

Müzeyyen ERTÜRK, Faik GÜRSOY, Vatan KARAKAYA

A STUDY ON LATERAL BASES AND COVERED LATERAL IDEALS OF ORDERED TERNARY SEMİGROUPS ............... 73

M. Yahya ABBASI, Sabahat Ali KHAN and Aakif Fairooze TALEE

APPROXIMATION PROPERTIES OF THE BERNSTEIN-CHLODOWSKY-DURRMEYER OPERATORS ON THE WHOLE

REEL AXIS .................................................................................................................................................... 74


11

Nadire Fulda ODABAŞI, Aydın İZGİ

ON 𝝀𝝂-STATISTICAL CONVERGENCE OF ORDER 𝜶 OF GENERALIZED DIFFERENCE SEQUENCES ........................ 75

Necip ŞİMŞEK, Mikail ET, Vatan KARAKAYA

ON THE DEFORMATION OF SOME BANACH SEQUENCE SPACES ..................................................................... 76

Ruken ÇELİK, Zhamile ASKEROVA, Necip ŞİMŞEK

ON KRAWTCHOUK POLYNOMIALS ................................................................................................................ 77

Nejla ÖZMEN

ASYMPTOTICALLY LACUNARY I-INVARIANT EQUIVALENCE OF SEQUENCES DEFINED BY A MODULUS FUNCTION

................................................................................................................................................................... 78

Nimet P. AKIN, Erdinç DÜNDAR and Uğur ULUSU

ASYMPTOTICALLY I-INVARIANT EQUIVALENCE OF SEQUENCES DEFINED BY A MODULUS FUNCTION ............. 79

Nimet P. AKIN, Erdinç DÜNDAR

ON FINITE DIMENSIONAL LEIBNIZ ALGEBRAS ................................................................................................ 80

Nil MANSUROĞLU, Mücahit ÖZKAYA

A NEW COMPLEX GENERALIZED BERNSTEIN-SCHURER OPERATOR ................................................................ 81

Nursel CETIN

LACUNARY 𝑰𝟐-INVARIANT CONVERGENCE OF DOUBLE SEQUENCES OF FUNCTIONS ON AMENABLE

SEMIGROUP ................................................................................................................................................ 82

Ömer KİŞİ, Erhan GÜLER

A GENERALIZED STATISTICAL CONVERGENCE VIA IDEALS DEFINED BY FOLNER SEQUENCE ON AMENABLE

SEMIGROUPS .............................................................................................................................................. 83

Ömer KİŞİ, Erhan GÜLER

ON THE NEW SOLUTIONS OF (3+1)-DIMENSIONAL POTENTIAL-YTSF EQUATION BY 𝒕𝒂𝒏𝑭𝝃𝟐-EXPANSION

METHOD ..................................................................................................................................................... 84

Ozlem KIRCI, Hasan BULUT

CONVERGENCE OF THE INVERSE CONTINUOUS WAVELET TRANSFORM IN WEIGHTED VARIABLE EXPONENT

AMALGAM SPACES ...................................................................................................................................... 85

Öznur KULAK, İsmail AYDIN

A NEW OPERATOR IDEAL ON BLOCK SEQUENCE SPACES ............................................................................... 86

Pınar ZENGİN ALP, Emrah Evren KARA

ON BICOMPLEX JACOBSTHAL-LUCAS NUMBERS ........................................................................................... 87

Serpil HALICI, Sevim ASLAN

ALGEBRA OF CONVERGENCE SET SEQUENCE ................................................................................................ 88

Sibel ÖZTÜRK and Harun POLAT

RESULTS ON A CLASS OF HARMONIC UNIVALENT FUNCTIONS INVOLVING A NEW DIFFERENTIAL OPERATOR . 89

Sibel YALÇIN TOKGÖZ, Şahsene ALTINKAYA

CERTAIN CONVEX HARMONIC FUNCTIONS DEFINED BY SUBORDINATION ..................................................... 90


CERTAIN SUBCLASSES OF HARMONIC UNIVALENT FUNCTIONS ASSOCIATED WITH A MULTIPLIER LINEAR

OPERATOR .................................................................................................................................................. 91


AN H-DEFORMATION OF SYMPLECTIC (1+2)-SUPERSPACE VIA A CONTRACTION ............................................. 92

Sultan Abaci CELIK, Canan AYDEMIR

ON A SUBCLASS OF BI-UNIVALENT FUNCTIONS WITH THE FABER POLYNOMIAL EXPANSIONS ........................ 93

Şahsene ALTINKAYA, Sibel YALÇIN

CHEBYSHEV POLYNOMIAL COEFFICIENT RESULTS ON A SUBCLASS OF ANALYTIC AND BI-UNIVALENT

FUNCTIONS INVOLVING QUASI-SUBORDINATION ......................................................................................... 94


ON THE BOUNDS OF GENERAL SUBCLASSES OF ANALYTIC AND BI-UNIVALENT FUNCTIONS ASSOCIATED WITH

SUBORDINATION ......................................................................................................................................... 95


12


STATISTICAL CONVERGENCE OF MINIMA AND MINIMIZERS OF SEQUENCES OF FUNCTIONS .......................... 96

Şükrü TORTOP, Yurdal SEVER and ÖZER TALO

ON THE Σ-STABLE FAMILIES .......................................................................................................................... 97

Taner BÜYÜKKÖROĞLU, Özlem ESEN, Vakıf CAFER

ON SOME ASYMPTOTICALLY EQUIVALENCE TYPES FOR DOUBLE SEQUENCES AND RELATIONS AMONG THEM

.................................................................................................................................................................. .98

Uğur ULUSU, Erdinç DÜNDAR

STATISTICAL LACUNARY INVARIANT SUMMABILITY OF DOUBLE SEQUENCES ................................................. 99

Uğur ULUSU, Esra GÜLLE

REDUCTION OF NAVIER-STOKES EQUATION TO A LINEAR EQUATION .......................................................... 100

Waleed KHEDR

EXTENDED KRYLOV METHOD FOR THE NUMERICAL RESOLUTION OF A LARGE SCALE DIFFERENTIAL SYMMETRIC

STEIN EQUATIONS ..................................................................................................................................... 101

Yaprak DERICIOGLU and Muhammet KURULAY

ON A NEW ESCAPE CRITERIONS FOR COMPLEX POLYNOMIALS USING FIXED POINT ITERATION METHOD AND S-

CONVEXITY ................................................................................................................................................ 102

Yunus ATALAN, Vatan KARAKAYA

A NEW ITERATION METHOD AND SOME FIXED POINT RESULTS ................................................................... 103

Yunus ATALAN

ON EXISTENCE AND UNIQUINESS OF SOME CLASS NONLINEAR EIGENVALUE PROBLEM ............................... 104

Yusuf ZEREN and Lutfi AKIN

OBTAINING THE FINITE DIFFERENCE APPROXIMATION OF TRANSMISSION CONDITIONS OF DEFORMATION

PROBLEM FOR MULTILAYERED MATERIALS ................................................................................................ 105

Zahir MURADOGLU, Vildan YAZICI, Tatsiana URBANOVICH

POSTER SESSION.......................................................................................................................................... 106

SUMS OF ELEMENT ORDERS IN FINITE GROUPS .......................................................................................... 106

Ayşe Nur KÖKSAL, Nil MANSUROĞLU

APPROXIMATION BY GENERALIZED COMPLEX SZÁSZ-MIRAKYAN OPERATORS IN COMPACT DISK................. 107

Döne KARAHAN, Sevilay K. SERENBAY, Aydın İZGİ

ON APPROXIMATION BY GENERALIZED BERNSTEIN-KANTOROVICH OPERATORS OF TWOVARIABLE ............ 108

Döne KARAHAN, Aydın İZGİ

NON PRESENTING PARTICIPANTS ................................................................................................................. 109

INDEX ........................................................................................................................................................... 110


13

PLENARY TALKS

EKELAND’S VARIATIONAL PRINCIPLE FOR SET-VALUED MAPS

Qamrul Hasan ANSARI

Department of Mathematics, Aligarh Muslim University, Aligarh, India

[email protected]

Abstract: The Ekeland variational principle (in short, EVP) is one the most applicable results from

nonlinear analysis and used as a tool to study the problems from fixed point theory, optimization,

optimal control theory, game theory, nonlinear equations, dynamical systems, etc. It was established

by Ekeland in 1972 and provides the existence of an approximate minimizer of a bounded below and

lower semicontinuous function defined on a complete metric space. Later, it is found that several

well-known results, namely, Caristi-Kirk fixed point theorem, Takahashi's minimization theorem,

Petal theorem and the Danes drop theorem, from nonlinear analysis are equivalent to the Ekeland's

variational principle. In 1981, Sullivan established that the conditions of EVP on a metric space (X,d)

imply the completeness of the metric space (X,d). In the last two decades, EVP has been generalized

in different directions, namely, it has been extended for bifunctions, called equilibrium version of

Ekeland’s variational principle; for vector-valued functions, for set-valued maps, etc.

The main aim of this talk is to discuss Ekeland varitaional principle for real-valued functions, for

vector-valued functions and for set-valued functions. We shall give some of our recent results on this

topic.

mailto:[email protected]


14

SOME RESULTS ON A COMMON ZERO OF A FINITE FAMILY OF ACCRETIVE

OPERATORS IN BANACH SPACES

Jong Kyu KIM

1Department of Mathematics Education, Kyungnam university,Changwon, Gyeongnam , 51767, Korea,

[email protected]

Abstract: In this talk, we introduce some new iterative methods to find a common zero of a finite

family of nonlinear operators in Banach spaces. We first introduce some strong convergence

theorems for the problem of finding a common zero of a finite family of monotone operators and also,

we give some problems of finding a common fixed point of a finite family of nonexpansive mappings

in Hilbert spaces by shrinking projection method. Next, we deal with strong convergence theorems

for finding a common zero of a finite family of accretive operators in Banach spaces with the weak

control conditions.

Keywords: Common zeros, monotone operators, accretive operators, shrinking projection method,

resolvent method, Halpern`s method.

References:

[1] J.K. Kim and T.M. Tuyen, Alternating resolvent algorithms for finding a common zero of two

accretive operator in Banach spaces, Jour. Korean Math. Soc. 54(6)(2017), 1905-1926.

[2] J.K. Kim and T.M. Tuyen, New iterative methods for finding a common zero of a finite family

of monotone operators in Hilbert spaces, Bull

Korean Math. Soc. 54(4)(2017), 1347-1359.

[3] J.K. Kim and T.M. Tuyen, Approximation common zero of two

accretive operators in Banach spaces, Applied Mathematics and Comput., 283(2016), 265-281.

[4] J.K. Kim and T.M. Tuyen, On the some regularization methods for

common fixed point of a finite family of nonexpansive mappings, Journal of Nonlinear and Convex

Analysis, Vol.17(1) (2016), 99-104.



15

APPLICATIONS OF MEASURES OF NONCOMPACTNESS TO MATRIX

TRANSFORMATIONS AND DIFFERENTIAL AND INTEGRAL EQUATIONS

Mohammad MURSALEEN

Department of Mathematics, Aligarh Muslim University, Aligarh/INDIA

[email protected]

Abstract: In this talk, we present a brief survey of theory and applications of measures of

noncompactness. The classical measures of noncompactness are discussed and their properties

are compared. The approaches for constructing measure of noncompactness in a general metric or

linear space are described, along with the classical results for existence of fixed point for condensing

operators. Also several generalization of classical results are mentioned and their applications in

various problems of analysis such as linear equation, di§erential equations, integral equations and

common solutions of equations are discussed. The most effective way in the characterization of

compact operators between the Banach spaces is applying the Hausdorff measure of

noncompactness. In this talk, we present some identities or estimates for the operator norms and

the Hausdorff measures of noncompactness of certain operators given by infinite matrices that map

an arbitrary BK-space into the sequence spaces 𝑐0, 𝑐 , 𝑙∞ and 𝑙1.Many linear compact operators may

be represented as matrix operators in sequence spaces or integral operators in function spaces [1].

Recently the measures of noncompactness are applied in solving infinite system of differential

equations [3] and integral equations in sequence spaces [2].

Keywords: Measures of noncompactness, differential equations, sequencespaces.

References:

[1] J. Banas and M. Mursaleen, Sequence Spaces and Measures of Noncompactness with

Applications to Differential and Integral Equations, Springer, 2014.

[2] Das, B. Hazarika, R. Arab and M. Mursaleen, Solvability of the infinite system of integral

equations in two variables in the sequence spaces c_0 and l_1, Jour. Comput. Appl. Math., 326

(2017) 183-192.

[3] M. Mursaleen and S.M.H Rizvi, Solvability of the infinite system of second order differential

equations in c_0 and l_1 by Meir-Keeler condensing operator. Proc. Amer.Math.Soc., 144 (10) (2016)

4279-4289.



16

PERTURBATION ANALYSIS FOR GENERALIZED INVERSES OF LINEAR

OPERATORS AND THE ROLE OF OUTER INVERSES IN REGULARIZATION

OF ILL-POSED PROBLEMS

Zuhair NASHED

Department of Mathematics, University of Central Florida, Orlando, Florida, USA

Abstract: Inverse Problems deal with determining for a given input-output system an input that

produces an observed output, or determining an input that produces an output that is as close as

possible to a desired output, often in the presence of noise. Most inverse problems are ill-posed, so

their resolution requires some methods of regularization.

Signal Analysis/Processing deals with digital representations of signals and their analog

reconstructions from digital representation.Sampling expansions, filters, reproducing kernel Hilbert

spaces, various function spaces, and techniques of functional analysis, computational and applied

harmonic analysis play pivotal role in this area.

This talk will highlight some land marks in these two areas and discuss some common threads

between them. We will show that function spaces, in particular reproducing kernel Hilbert spaces,

play a magical role in bothill-posed inverse problems and sampling expansion theorems.

The year 2016 marks the 110th birthday of the great Russian mathematician Andrey Nikoayevich

Tikhonov (October 30, 1906 - October 7, 1993) and the 100th birthday of the great American

mathematician Claude Elwood Shannon (April 30, 1916 - February 24, 2001). We celebrate their

memory and seminal contributions to regularization theory of ill-posed problems, and sampling

expansions and communication theory, respectively.


17

RIEMANNIAN MAPS IN KAEHLER GEOMETRY

Bayram ŞAHİN

Ege University, Department of Mathematics, 35100, Izmir, Turkey.

[email protected]

Abstract: Riemannian maps were introduced by Fischer in [4] as a generalization of isometric

immersions and Riemannian submersions. Later such maps have been considered from (to) Kaehler

manifolds ( see [5] for detais) as generalizations of holomorphic submanifolds, totally real

submanifolds [6], CR-submanifolds [1], generic submanifolds [2], slant submanifolds[3], holomorphic

submersions, anti-invariant Riemannian submersions, semi-invariant Riemannian submersions,

generic submersions, slant submersions [5]. In this talk, we survey recent results on the geometry

of Riemannian maps from (to) Kaehler manifolds and give several examples.

References:

[1] A.Bejancu, Geometry of CR-submanifolds, Kluwer, 1986.

[2] B.Y.Chen, Geometry of submanifolds and Its applications, Science University of Tokyo, 1981.

[3] B.Y.Chen, Geometry of Slant Submanifolds, Katholike University, Leuven, 1990.

[4] A.E.Fischer, Riemannian Maps Between Riemannian Manifolds, Contemporary Mathematics,

132, 1992.

[5] B.Şahin, Riemannian Submersions, Riemannian Maps in Hermitian Geometry and Their

Applications, Elsevier, 2016.

[6] K. Yano,M.Kon, Structures on Manifolds, World Scientific, 1984.



18

Contributed Talks

ROOTS OF ANALYSIS IN ISLAMIC MATHEMATICS

Abdulmajid NUSAYR

Professor Emeritus

Jordan University of Science and Technology

Abstract: Mathematics like other fields of knowledge is cumulative. The roots of mathematical

analysis may be traced to the earlier mathematical activities as may be understood in Egyptian,

Mesopotamian and Greek mathematics. However, these aspects were none direct and ambiguous.

When we come to Islamic era we find these roots are clear and applicable. We shed light on three

fields where Islamic mathematicians treated analysis loud and clear. We look into the works of Al-

Hasan (Al-hazen) ibn Al-Haitham and his famous problem; arithmatization of al-Jabr by al-Karji and

the use of first derivative to find extremum values by Abu- Muzaffar Altusi.

جذور التحليل الرياضي في الرياضيات اإلسالمية

عبد المجيد نصير

أستاذ الشرف

جامعة العلوم والتكنولوجيا األردنية

الرياضية في رياضيات الرياضيات معرفة تراكمية، شأنها كغيرها من المعارف. ويمكن تتبع جذور التحليل الرياضي إلى بدايات النشاطات

المصريين وما بين النهرين واإلغريق. لكن هذه المالمح كانت غير مباشرة وغامضة. وعندما نأتي إلى الرياضيات اإلسالمية نجد هذه الجذور

في مسألة واضحة ومطبقة. في هذا البحث نلقي الضوء على ثالثة مجاالت تعامل الرياضيون اإلسالميون مع التحليل بقوة ووضوح. سننظر

الحسن )الحسن بن الهيثم( الشهيرة، وحسبنة الجبر لمحمد الكرجي، وإيجاد القيم القصوى باستعمال المشتقة األولى ألبي المظفر الطوسي.


19

WAVELET PACKET TRANSFORMATION ASSOCIATED WITH LINEAR

CANONICAL HANKEL TRANSFORMATION

Akhilesh PRASAD, Tanuj KUMAR

Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines),Dhanbad.

826004, Jharkhand, India.

[email protected]

[email protected]

Abstract: The main goal of this paper is to construct wavelet packet transformation in terms of linear

canonical Hankel transformation and discuss some of its basic properties. An inversion formula for

linear canonical wavelet packet transformation is also obtained. Some examples are also discussed.

Keywords: Linear canonical Hankel wavelet, Convolution, Translation.




20

CONVERGENCE THEOREMS FOR SOME MAPPINGS IN A TYPE OF

PROBABILISTIC NORMED SPACES

Arife Aysun KARAASLAN1, Vatan KARAKAYA2

1Department of Mathematics, Işık University, İstanbul/TURKEY

[email protected]

2Department of Mathematical Engineering, Yıldız Technical University, İstanbul/TURKEY

[email protected]

Abstract: In this presentation, we obtain the definition of probabilistic demicontractive mapping in a

S-probabilistic normed space. Also, probabilistic convergence theorems for these mappings are

proved.

Keywords: Probabilistic normed space, demicontractive mapping, fixed point.

Acknowledgement: The first author was supported by TÜBİTAK- The Scientific and Technological

Research Council of Turkey.

References:

[1] Xu Y., Guan J., Su Y., Weak and Strong Convergence Theorems of Fixed Points for

Nonexpansive Mappings and Strongly Pseudocontractive Mappings in a New Class of Probabilistic

Normed Spaces, Fixed Point Theory and Applications, 2015.

[2] Alsina C., Schwizer B., Sklar A., On the Definition of Probabilistic Normed Space. Aequ.

,Math., 46, 91-98 (1993).



21

ON GENERALIZED TRIBONACCI OCTONIONS

Arzu ÖZKOÇ ÖZTÜRK

Düzce University, Faculty of Art and Science, Department of Mathematics, Düzce, Turkey

[email protected]

Abstract: In this work, we investigate the properties of generalized tribonacci octonions over the

octonion algebra. After presenting generating functions and Binet formulas, we obtain some

properties of these types of octonions.

Keywords: Binet formulas, octonion, generating functions, generalized tribonacci sequence.

References:

[1] Koshy T., Fibonacci and Lucas Numbers with Applications, Wiley Intersection Pub., New York,

2001.

[2] Cerda-Morales G., "The Third order Jacobsthal Octonions: Some Combinatorial Properties.’’ https://arxiv.org/abs/1710.00602.pdf.

[3] Akkuş I. and Kizilaslan G., "On Some Properties of Tribonacci Quaternions.’’

https://arxiv.org/pdf/1708.05367.pdf.

[4] Çimen C.B. and Ipek A., "On Jacobsthal and Jacobsthal-Lucas Octonions. ’’ Mediterranean

Journal of Mathematics, 14:37 (2017), 1–13.

[5] Cerda-Morales G., "On a Generalization for Tribonacci Quaternions.’’ Mediterranean Journal of

Mathematics, 14:239(2017)1-12.

[6] Catarino P., "The modified Pell and the modified k-Pell quaternions and octonions. " Adv. Appl.

Clifford Algebras, 26 (2016), 577–590.

[7] Pethe S., "Some Identities for Tribonacci Sequences." The Fibonacci Quarterly, 26(2) (1988),

144–151.

[8] Feinberg M., "Fibonacci-Tribonacci." The Fibonacci Quarterly, 1(3) (1963), 71–74.

[9] Flaut C. and Shpakivskyi V., "On Generalized Fibonacci Quaternions and Fibonacci-Narayana

Quaternions." Adv. Appl. Clifford Algebras, 23(3)(2013), 673-688.


https://arxiv.org/abs/1710.00602.pdf

https://arxiv.org/pdf/1708.05367.pdf


22

SOME INVESTIGATIONS FOR TIME FRACTIONAL KORTEWEG-DE VRIES

EQUATION USING THE FINITE DIFFERENCE METHOD

Asıf YOKUS

Department of Actuary, Firat University, Elazig, 23200, Turkey

[email protected]

Abstract: In the present work, by using the (1/G')-expansion method and the finite forward difference

method the non-linear time fractional Korteweg-de Vries equation is studied by obtaining the exact

wave solutions of the non-linear time fractional Korteweg-de Vries equation. The index forms for

some derivatives of certain types are considered. It is observed that that the obtained numerical

results approach to the exact solution.

Keywords: Time fractional KdV equation, Finite difference method, Traveling wave solutions

References:

[1] A. Yokus, Solutions of Some Nonlinear Partial Differential Equations and Comparison of Their

Solutions, Ph.D. Thesis, Firat University, (2011).

[2] W. Chen, L. Ye and H. Sun, Fractional di_usion equations by the Kansa method, Comput. Math.

Appl. 59 1614-1620 (2010).

[3] M. Yavuz, N. Ozdemir,New numerical techniques for solving fractional partial differential

equations in conformable sense In Conference on Non-integer Order Calculus and Its Applications,

49-62 Springer, Cham (2017).



23

SOME NEW RESULTS OF M-ITERATION PROCESS IN HYPERBOLIC

SPACES

Aynur ŞAHİN

Department of Mathematics, Sakarya University, 54050 Sakarya, Turkey

[email protected]

Abstract: In this study, the strong convergence and weak 2w -stability theorems are proved for M-

iteration process in hyperbolic spaces. Under some suitable conditions, the data dependence result

of this iteration for a class of contractive-type mappings is also established. The results presented

here extend and improve some recent results announced in the current literature.

Keywords: Fixed point, stability, data dependence, hyperbolic space, contractive-type mapping, M-

iteration process.

References:

[1] Ullah, K, Arshad, M: Numerical reckoning fixed points for Suzuki’s generalized nonexpansive

mappings via new iteration process. Filomat 32:1 (2018), 187-196.

[2] Timiş, I: On the weak stability of Picard iteration for some contractive type mappings. Annal.

Uni. Craiova, Math. Comput. Sci. Series, 37:2 (2010), 106-114.

[3] Kohlenbach, U: Some logical metatheorems with applications in functional analysis. Trans.

Amer. Math. Soc. 357 (2004), 89-128.

[4] Osilike, M. O, Udomene, A: Short proofs of stability results for fixed point iteration procedures

for a class of contractive-type mappings. Indian J. Pure Appl. Math. 30:12 (1999), 1229-1234.

[5] Şahin, A, Başarır, M: Convergence and data dependence results of an iteration process in a

hyperbolic space. Filomat 30:3 (2016), 569-582.

[6] Gürsoy, F, Khan, A. R, Ertürk, M, Karakaya, V: Weak 2w -stability and data dependence of

Mann iteration method in Hilbert spaces, RACSAM (2017), doi: 10.1007/s13398-017-0447-y.



24

DG SOLUTION OF DIFFUSION-REACTION PROBLEM TO MODEL THE

DENSITY OF TUMOR GROWTH DYNAMIC

Ayşe SARIAYDIN-FİLİBELİOĞLU

Scientific and Technological Research Council of Turkey (TÜBİTAK), Tunus Caddesi, No: 80, 06100

Kavaklıdere, Ankara, Turkey,

[email protected]

Abstract: In this work, we numerically solve diffusion-reaction problem modeling the density of the

tumor growth dynamics. We employ a nonlinear heterogeneous diffusion logistic density model [1].

This model assumes that glioma cell invasion throughout the brain is a reaction-diffusion process

and the coefficient of diffusion can vary according to the gray and white matter composition of the

brain at that location. To visualize and investigate numerically the behavior of the evolution of tumor

concentration of the glioma, we propose an efficient discontinuous Galerkin finite elements method

(DGFEM) [2] in space and implicit Euler method in time to solve the equation. Numerical examples

demonstrate effectiveness of the method.

Keywords: diffusion-reaction equation, discontinuous Galerkin, tumor growth.

References:

[1] E. Özuğurlu, A note on the numerical approach for the reaction-diffusion problem to model the

density of the tumor grwoth dynamics. Computers and Mathematics with Applications, 69 (2015),

1504-1517.

[2] B. Rivière, Discontinuous Galerkin methods for solving elliptic and parabolic equations,

Frontiers in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM),

Philadelphia, PA, 2008.



25

NOTES ON GENERATED q-POLY GENOCCHI POLYNOMIALS

Burak KURT

Department of Mathematics, Akdeniz University,07070 Antalya, Turkey,

[email protected]

Abstract: In recently years, many mathematicians studied q-Bernoulli polynomials, q-Euler

polynomials, q-Genocchi polynomials, poly-Bernoulli, poly-Euler and poly-Genocchi polynomials and

numbers. They investigated and defined some properties of these polynomials. They proved some

symmetric relations for these polynomials. Mahmudov introduced q-Bernoulli polynomials and q-

Genocchi polynomials. Kim et al. introduced poly-Genocchi polynomials. They gave some recurrence

relation for the higher-order poly-Bernoulli polynomials. In this work, we give basic relation for the

generalized q-poly-Genocchi polynomials. We give different relations between the q-poly-Genocchi

polynomials and the Stirling numbers of the second kind.

Keywords: genocchi polynomails and numbers, poly-genocchi polynomials, generating functions.

References:

[1] A. Bayad and Y. Hamahata: “Polylogarithms and poly-Bernoulli polynomials”. Kyushu J. Math.

65 (2011):15-34.

[2] D. Kim and T. Kim: “A note on poly-Bernoulli and higher order poly-Bernoulli polynomials.”

Russian J. of Math. Physics. 22.1 (2015): 26-33.

[3] N. I. Mahmudov: “q-Analogues of the Bernoulli and Genocchi polynomials and the Srivastava-

Pinter addition theorem.” Discrete Dyn. In Natue and Society. Aricle ID:169348. (2012).

[4] H. M. Srivastava: “Some generalization and basic (or q-) extension of the Bernoulli, Euler and

Genocchi Polynomials.” Appl. Math. Inform. Sci. 5 (2011): 390-444.


https://www.seslisozluk.net/mathematician-nedir-ne-demek/


26

THINNESS AND FINE TOPOLOGY WITH RELATIVE CAPACITY

Cihan UNAL1, Ismail AYDIN2

1,2Faculty of Arts and Sciences, Department of Mathematics, Sinop University, 57000 Sinop, Turkey,

[email protected]

[email protected]

Abstract: In this study, we present a thinness with relative capacity for weighted variable exponent

Sobolev spaces. Also, we investigate some properties of finely sets in sense to this thinness.

Moreover, we consider fine topology which is finer than Euclidean topology.

Keywords: Fine topology, Thinness, Relative capacity.

References:

[1] I. Aydın, Weighted variable Sobolev spaces and capacity, J. Funct. Spaces Appl., 2012, Article

ID 132690, (2012)

[2] P. Harjulehto, V. Latvala, Fine topology of variable exponent energy superminimizers, Ann.

Acad. Sci. Fenn.-M., 33, 491-510, (2008)

[3] P. Harjulehto, P. Hästö, M. Koskenoja, Properties of capacities in variable exponent Sobolev

spaces, J. Anal. Appl., 5(2), 71-92, (2007)

[4] J. Heinonen, T. Kilpeläinen, O. Martio, Nonlinear Potential Theory of Degenerate Elliptic

Equations, Oxford University Press, Oxford, (1993)

[5] C. Unal, I. Aydın, On some properties of relative capacity and thinness in weighted variable

exponent Sobolev spaces (Submitted)




27

ON APPLICATIONS OF MULTIDIMENSIONAL AFFINE TRANSFORM IN THE

SUPPLY OF MISSING DATA

Cuneyt YAZICI1, Suleyman CETINKAYA2, Hulya KODAL SEVİNDİR3

1,2,3Department of Mathematics Education, Kocaeli University, Umuttepe Campus, İzmit, 41380 Kocaeli,

Turkey,

[email protected]

[email protected]

[email protected]

Abstract: Supply of missing data is one of the image processing applications. Shearlet transform,

which is an important affine transformation, can be used for multivariate data analysis. In this study,

we used shearlet transform in the supply of missing data and we compared the obtained results.

Keywords: supply of missing data, image processing, shearlet, multivariate data.

References:

[1] Kutyniok G., Lim W. Q., “Image Separation Using Wavelets and Shearlets”, Curves and

Surfaces, 6920, 416-430, 2012.

[2] Q., Guo, S., Yu, X., Chen, C., Liu and W.,Wei, “Shearlet-based Image Denoising Using Bivariate

Shrinkage with Intra-band and Opposite Orientation Dependencies”, IEEE Conference Publications,

1, 863–866, 2009.

[3] G. R., Easley and D., Labate, “Image Processing Using Shearlets”, Editors: G., Kutyniok and D.,

Labate Shearlets: Multiscale Analysis for Multivariate Data, Birkhäuser, Boston, 283–325, 2012.

[4] E. J., King, G., Kutyniok and Zhuang X., ““Analysis of Inpainting via Clustered Sparsity and

Microlocal Analysis”, J.Math. Imaging Vis., 48, 205–234, 2014.





28

DIMENSION OF PRODUCT OF FOUR HOMOGENEOUS COMPONENTS IN

FREE LIE ALGEBRAS

Derya KARATAŞ1, Nil MANSUROĞLU2

1,2Department of Mathematics, Kırşehir Ahi Evran University, 40100 Kırşehir, Turkey,

[email protected]

[email protected]

Abstract: Let L be a free Lie algebra of rank ≥ 2 over a field F and let 𝐿𝑛 denote the degree n

homogeneous component of L. In this study, firstly we give that how to calculate the dimension of 𝐿𝑛

and product of two and the dimension of three homogeneous components in free Lie algebra. Then

we show that how to determine the dimension of products of four homogeneous components in free

Lie algebra L.

Keywords: free Lie algebra, homogeneous subspaces, homogeneous components, Witt formula,

free generators.

References:

[1] N. Mansuroğlu, Products of homogeneous subspaces in free Lie algebra, MSc thesis, University

of Manchester, 2010.

[2] N. Mansuroğlu, R. Stöhr, On the dimension of products of homogeneous subspaces in free Lie

algebras, Internat J. Algebra Comput, 23 (2013): 205-213.

[3] R. Stöhr and M. Vaughan-Lee, Products of homogeneous subspaces in free Lie algebras,

Internat J. Algebra Comput, 19 (2009): 699-703.

[4] E. Witt, Treue Darstellungen Liescher Ringe, J. Reine Angew. Math. 177 (1937): 152-160.



29

ON THE F-CONTRACTION OF THE DARBO THEOREM GENERALIZED BY

FUNCTION CLASSES

Derya SEKMAN1, Vatan KARAKAYA2

1Department of Mathematics, Ahi Evran University, Bagbasi Campus, 40100 Kirsehir, Turkey,

[email protected]

2 Department of Mathematical Engineering, Yildiz Technical University, Davutpasa Campus, Esenler, 34210

Istanbul, Turkey,

[email protected]

Abstract: Darbo’s fixed point theory has been studied and generalized with many different concepts.

In this work, we will investigate the behavior and the existence of a fixed point under F-contraction

of the theorem expanded by function classes.

Acknowledgement: This work was supported by the Ahi Evran University Scientific Research

Projects Coordination Unit. Project Number: RKT.A3.17.001.

Keywords: Darbo fixed point theorem, shifting distance function, F-contraction

References:

[1] J. Banas, K. Goebel, Measure of Noncompactness in Banach Spaces, Lecture Notes in Pure

and Applied Mathematics 60, Dekker, New York, 1980.

[2] M. Berzig, Generalization of the Banach Contraction Principle (2013), arXiv:1310.0995

[math.CA].

[3] A. Samadi and M.B. Ghaemi, An Extension of Darbo’s Theorem and Its Application, Abstract

and Applied Analysis 2014 (2014), Article ID 852324, 11 pages.

[4] D. Wardowski, Fixed Points of A New Type of Contractive Mappings In Complete Metric

Spaces, Fixed Point Theory and Appl. 2012, 2012: 94.




30

ISHIKAWA ITERATION PROCESS AS CONTROL SYSTEMS AND CHAOTIC

DISCRETE DYNAMICAL SYSTEMS

Derya SEKMAN1, Vatan KARAKAYA2

1Department of Mathematics, Ahi Evran University, Bagbasi Campus, 40100 Kirsehir, Turkey,

[email protected]


Istanbul, Turkey,

[email protected]

Abstract: In this study, chaos structures of dynamics which are formed by applying Ishikawa iteration

processes to function classes with chaotic behavior in discrete dynamic systems have been

investigated. Later, the control mechanisms for chaotic structures have been developed according

to the stable and unstable state of fixed points of this transformation.

Acknowledgement: This work was supported by the Yildiz Technical University Scientific Research

Projects Coordination Unit. Project Number: FDK-2018-3348

Keywords: Discrete dynamical system, chaotical structure, control mechanism, Ishikawa iteration

References:

[1] Berinde, V., Controlling chaotic dynamical systems through fixed point iterative techniques,

"Vasile Alecsandri" University of Bacau Faculty of Sciences Scientific Studies and Research Series

Mathematics and Informatics, Vol. 19 (2009), No. 2, 47-58.

[2] Huang, W., Controlling chaos through growth rate adjustment, Discrete Dyn. Nat.Soc., 7 (3),

191-199, 2002.

[3] Deng, L., Ding, X.P., Ishikawa's Iterations Of Real Lipschitz Functions, Bull. Austral. Math. Soc.,

Vol. 46 (1992): 107-113.

[4] B.E. Rhoades, 'Comments on two fixed point iteration methods', J. Math. Anal. Appl. 56 (1976),

741-750.




31

SYMMETRY ANALYSIS AND CONSERVATION LAWS OF THE BOUNDARY

VALUE PROBLEMS FOR TIME-FRACTIONAL GENERALIZED BURGERS'

DIFFERENTIAL EQUATION

Dogan KAYA1, Gulistan ISKANDAROVA2

1,2 Department of Mathematics, Istanbul Commerce University, Faculty of Art and Science, 34445 Istanbul,

Turkey,

[email protected]

[email protected]

Abstract: In this work we obtain symmetries of the boundary value problem for fractional nonlinear

generalized Burgers’ differential equation [1, 2]. And find some exact solutions of the nonlinear

generalized Burgers’ differential equation with fractional derivative by using symmetry method [3, 4].

Also we found conservation laws for the nonlinear generalized Burgers’ differential equation.

Keywords: Burgers’ equation, Boundary value problem, Symmetry analysis, conservations laws,

Riemann--Liouville fractional derivative.

References:

[1] Olver P., Applications of Lie groups to differential equations, Springer Science, Germany, 2012.

[2] Ibragimov N., CRC Handbook of Lie Group Analysis of Differential Equations, CRC Press, Boca

Raton, 1994.

[3] Gazizov R.K, Kasatkin A.A., and Lukashchuk S.Y, Continuous transformation groups of

fractional differential equations. Vestn. USATU, 9, 125-135 (2007).

[4] Iskandarova G, and Kaya D, Symmetry solution on fractional equation, IJOCTA, 7(3), 255-259

(2017).




32

SOME REMARKS RELATED TO CONTRACTION MAPPINGS ON F-METRIC

SPACES

Emrah Evren KARA1, Merve İLKHAN2

1,2Department of Mathematics, Düzce University, Düzce, Turkey,

[email protected]

[email protected]

Abstract: The purpose of this study is to prove some fixed point theorems with regard to special kind

of self-mappings on a newly introduced generalized metric space.

Keywords: fixed point, contraction mappings, F-metric spaces.

References:

[1] E. Rakotch: A note on contractive mappings, Proc. Amer. Math. Soc. 13, 459-465 (1962)

[2] S. P. Singh and W. Russel, A note on a sequence of contraction mappings, Canad. Math. Bull.

12, 513-516 (1969)

[3] R. Kannan, Some results on fixed points-II, Amer. Math. Monthly 76, 405-408 (1969)

[4] S. Reich: Some remarks concerning contraction mappings, Canad. Math. Bull. 14(1), 121-124

(1971)




33

SOME NEW INEQUALITIES AND HERMITE-HADAMARD-FEJER INEQUALITY

VIA NON-NEWTONIAN CALCULUS

Erdal ÜNLÜYOL1, Yeter ERDAŞ2

1,2Department of Mathematics, Ordu University, 52200, Ordu, Turkey,

[email protected]

[email protected]

Abstract: In this study, Hermite-Hadamard-Fejer inequality is expressed and proved in Non-

Newtonian calculus. Then, some new inequalities have been achieved by carrying out Non-

Newtonian calculus of inequality structures that have been generalized using Hermite-Hadamard-

Fejer.

Keywords: Hermite-Hadamard-Fejer inequality, Non-Newtonian calculus.

Acknowledgment: In this study supported by Ordu University Scientific Research number of B-1803

References:

[1] Michael Grosmann and Robert Katz, Non- Newtonian Calculus, Lee Press Pigeon Cove,

Massachusetts (1972).

[2] Agamirza E. Bashirov, Emine Mısırlı Kurpınar, Ali Özyapıcı, Multiplicative calculus and its

applications, J. Math. Anal. Appl. 337, 36–48 (2008).

[3] Uğur Kadak, Newtonyen olmayan analiz ve uygulamaları, Dr. Tezi, Gazi Üniversitesi, (2015).

[4] Erdal Ünlüyol, Seren Salaş, İmdat İşcan, Convex functions and some inequalities in terms of

the Non-Newtonian Calculus April 2017,AIP Conference Proceedings 1833(1):020043,

DOI,10.1063/1.4981691, (2017).

[5] Erdal Ünlüyol, Seren Salaş, İmdat İşcan, A new view of some operators and their properties in

terms of the Non-Newtonian Calculus Topol. Algebra Appl. 2017 (5), 49-54,

https://doi.org/10.1515/taa-2017-0008, (2017).




34

ASYMPTOTICALLY 𝑰𝟐-INVARIANT EQUIVALENCE OF DOUBLE SEQUENCES

AND SOME PROPERTIES

Erdinç DÜNDAR, Uğur ULUSU and Fatih NURAY

Department of Mathematics, Afyon Kocatepe University, 03200, Afyonkarahisar, Turkey,

[email protected]

[email protected]

[email protected]

Abstract: In this paper, we give definitions of asymptotically ideal equivalent, asymptotically invariant

equivalent and strongly asymptotically invariant equivalent for double sequences. Also, we give

some properties and examine the existence relationships among these new type equivalence

concepts.

Keywords: asymptotically equivalence, double sequence, ideal convergence, invariant

convergence, ideal invariant equivalence.

References:

[1] E. Dündar, U. Ulusu and F. Nuray, On ideal invariant convergence of double sequences and

some properties, Creat. Math. Inform. 27(2) (2018), 161-169.

[2] B. Hazarika, V. Kumar, On asymptotically double lacunary statistical equivalent sequences in

ideal context, Journal of Inequalities and Applications, 2013:543 (2013), 1-15.

[3] P. Kostyrko, T. Salat and W. Wilczynski, I-Convergence, Real Anal. Exchange, 26(2) (2000),

669-686.

[4] M. Marouf, Asymptotic equivalence and summability, Int. J. Math. Math. Sci. 16(4) (1993), 755-

762.




35

HELICOIDAL HYPERSURFACES OF DINI-TYPE IN THE FOUR DIMENSIONAL

MINKOWSKI SPACE

Erhan GÜLER1, Ömer KiŞi2

1,2Bartın University, Faculty of Science, Department of Mathematics, 74100 Bartın, Turkey

[email protected]

[email protected]

Abstract: In this talk, we consider Italian Mathematician Ulisse Dini’s type helicoidal surfaces in the

three dimensional Euclidean space and then we extend it to the helicoidal hypersurfaces of Dini-type

in the four dimensional Minkowski space. There are three types, depending on the axis of rotation in

Minkowski geometry. Equations for the Gaussian and mean curvature are derived and some

examples of the various types of hypersurfaces are given.

Keywords: Helicoidal hypersurfaces of Dini-type, Gaussian curvature, mean curvature, Minkowski

4-space.

References:

[1] K. Arslan, R. Deszcz, Ş. Yaprak, On Weyl pseudosymmetric hypersurfaces. Colloq. Math. 72-

2, 353-361 (1997).

[2] B.Y. Chen, Total mean curvature and submanifolds of finite type. World Scientific, Singapore,

1984.

[3] U. Dini, Sopra le funzioni di una variabile complessa, Annali di matematica pura ed applicate.

4(2), 159-174; in [Dini, Opere, II, 245-263] (1871).

[4] E. Güler, A. Gümüşok Karaalp, M. Magid, Dini-type helicoidal hypersurface in 4-space

(submitted).

[5] E. Güler, H.H. Hacısalihoğlu, Y.H. Kim, The Gauss map and the third Laplace-Beltrami operator

of the rotational hypersurface in 4-space (submitted).

[6] E. Güler, G. Kaimakamis, M. Magid, Helicoidal hypersurfaces in Minkowski 4-space E₁⁴

(submitted).

[7] E. Güler, M. Magid, Y. Yaylı, Laplace Beltrami operator of a helicoidal hypersurface in four

space. J. Geom. Sym. Phys. 41, 77-95 (2016).

[8] E. Güler, N.C. Turgay, Cheng-Yau operator and Gauss map of rotational hypersurfaces in 4-

space (submitted).

[9] M. Magid, C. Scharlach, L. Vrancken, Affine umbilical surfaces in R⁴. Manuscripta Math. 88,

275-289 (1995).




36

TORUS HYPERSURFACE IN 4-SPACE

Erhan GÜLER1, Ömer KiŞi2


[email protected]

[email protected]

Abstract: Torus hypersurface is defined in the four dimensional Euclidean space. Equations for the

Gaussian and mean curvature are derived and some examples of the projection surfaces are given.

Keywords: Torus hypersurface, Gaussian curvature, mean curvature, Euclidean 4-space.

References:

[1] Abbena,E. Salamon S., Gray A. Modern Differential Geometry of Curves and Surfaces with

Mathematica, Chapman and Hall/CRC, 2006.

[2] Banchoff T.F., Lovett S.T. Differential Geometry of Curves and Surfaces. A K Peters/CRC

Press, 2010.

[3] Chen B.Y. Total mean curvature and submanifolds of finite type. World Scientific, Singapore,

1984.

[4] Cheng, Q.M. Wan, Q.R. Complete hypersurfaces of R⁴ with constant mean curvature. Monatsh.

Math. 118 3-4, 171-204 (1994).

[5] Cheng S.Y., Yau S.T. Hypersurfaces with constant scalar curvature. Math. Ann., 225 195—204

(1977).

[6] Dillen F., Pas J., Verstraelen L. On surfaces of finite type in Euclidean 3-space. Kodai Math. J.

13, 10-21 (1990).

[7] Do Carmo M., Dajczer M. Rotation Hypersurfaces in Spaces of Constant Curvature. Trans.

Amer. Math. Soc. 277, 685-709 (1983).

[8] Ferrandez A., Garay O.J., Lucas P. On a certain class of conformally at Euclidean

hypersurfaces. Proc. of the Conf. in Global Analysis and Global Differential Geometry, Berlin, 1990.

[9] Ganchev G., Milousheva V. General rotational surfaces in the 4-dimensional Minkowski space.

Turkish J. Math. 38, 883-895 (2014).

[10] Magid M., Scharlach C., Vrancken L. Affine umbilical surfaces in R⁴. Manuscripta Math. 88

(1995) 275-289.

[11] Moore C. Surfaces of rotation in a space of four dimensions. Ann. Math. 21 (1919) 81-93.

[12] Moore C. Rotation surfaces of constant curvature in space of four dimensions. Bull. Amer. Math.

Soc. 26 (1920) 454-460.




37

ON QUASI-LACUNARY INVARIANT CONVERGENCE OF SEQUENCES OF

SETS

Esra GÜLLE, Uğur ULUSU


[email protected] [email protected]

Abstract: In this study, we give definitions of Wijsman quasi-lacunary invariant convergence,

Wijsman strongly quasi-lacunary invariant convergence and Wijsman quasi-lacunary invariant

statistically convergence for sequences of sets. We also examine the existence of some relations

among these definitions and some convergences types for sequences of sets given in [4, 5], too.

Keywords: statistical convergence, invariant convergence, quasi-invariant convergence, lacunary

sequence, sequences of sets, Wijsman convergence.

References:

[1] G.Beer, Wijsman convergence: A survey, Set-Valued Analysis, 2 (1994), 77-94.

[2] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.

[3] J. A. Fridy and C. Orhan, Lacunary statistical convergence, Pacific Journal of Math. 160(1)

(1993), 43-51.

[4] E. Gülle and U. Ulusu, Wijsman quasi-invariant convergence, Filomat, (submitted for publication).

[5] N. Pancaroğlu and F. Nuray, Lacunary invariant statistical convergence of sequences of sets with

respect to a modulus function, Journal of Mathematics and System Science, 5 (2015), 122-126.

[6] R. A. Raimi, Invariant means and invariant matrix methods of summability, Duke Math. J. 30(1)

(1963), 81-94.



38

SOME FIXED POINT RESULTS FOR A NEW THREE STEPS ITERATION

PROCESS IN BANACH SPACES: A REVISIT

Faik GÜRSOY1, Müzeyyen ERTÜRK2, Vatan KARAKAYA3

1,2Department of Mathematics, Adiyaman University,02040 Adiyaman, Turkey,

[email protected]

[email protected]


Istanbul,Turkey,

[email protected]

Abstract: In this presentation, a recently published paper by Karakaya et al. [Some fixed point results

for a new three steps iteration process in Banach spaces, Fixed Point Theory, 18 (2017), No. 2, 625-

640] revisited. The obtained results in this revisit are substantially improve the results reported in the

mentioned paper.

Keywords: Almost contraction mappings, three-step iterative algorithm, strong convergence, data

dependency.

References:

[1] Karakaya, V, Atalan, Y, Doğan, K, El Houda Bouzara, N, Some fixed point results for a new

three steps iteration process in Banach spaces, Fixed Point Theory 18, 625-640 (2017)





39

AN APPLICATION OF THREE DIMENSIONAL CELLULAR AUTOMATA

WITH PBC

Ferhat SAH

Department of Mathematics, Adiyaman University, Adiyaman, Turkey,

[email protected]

Abstract: In this study we give an application of CA based bit error correcting codes by applying

reversible CA which fall into a 3D-CA family with periodic boundary condition. we also compare the

classical syndrome decoding with the one introduced

Keywords: error correcting codes, periodic boundary condition, characteristic matrix

References:

[1] D.R. Chowdhury, S. Basu, I.S. Gupta and P.P. Chaudhuri, Design of CAECC- Cellular Automata

Based Error Correcting Code,IEEE Trans. Computers, 43 (1994) 759-764.

[2] M.E.Koroglu, I.Siap and H. Akın, Error correcting codes via reversible cellular automata over

finite fields, The Arabian Journal for Science and Engineering, vol.39, pp.1881-1887, (2014)

[3] Siap, I., Akin, H., and Koroglu, M. E. Reversible cellular automata with penta- cyclic rule and

ECCs. International Journal of Modern Physics C, 23(10), 1250066, (2012).



40

AN APPLICATION OF ONE DIMENSIONAL CELLULAR AUTOMATA UNDER

INTERMEDIATE BOUNDARY CONDITION

Ferhat SAH

Department of Mathematics, Adiyaman University, Adiyaman, Turkey,

[email protected]

Abstract: In this study we give some important definitions and then we talk about some dvantages

error correcting codes and its applications.Finally, we present an application of CA based bit error

correcting codes by applying reversible CA which fall into a CA family with inter-mediate boundary

condition.

Keywords: error correcting codes, periodic boundary condition,

characteristic matrix

References:

[1] D.R. Chowdhury, S. Basu, I.S. Gupta and P.P. Chaudhuri, Design of CAECC-Cellular Automata

Based Error Correcting Code, IEEE Trans. Computers, 43 (1994) 759-764.

[2] M.E.Koroglu, I.Siap and H. Akın, Error correcting codes via reversible cellular automata over

finite fields, The Arabian Journal for Science and Engineering, vol.39,pp.1881-1887, (2014)

[3] Siap, I., Akin, H., and Koroglu, M. E. Reversible cellular automata with penta- cyclic rule and

ECCs. International Journal of Modern Physics C, 23(10), 1250066, (2012).



41

NUMERICAL APPROACH BASED ON LAGRANGE POLYNOMIALS FOR

SOLVING FREDHOLM INTEGRAL EQUATIONS

Fernane KHAIREDDINE

Department of Mathematics, Laboratory of Applied Mathematics and Modeling,University of 8 May 1945

Guelma, Algeria

[email protected]

Abstract: In this paper, we introduce a numerical method for solving linear Fredholm integral

equations of the second type. To solve these equations, we consider the equation solution

approximately from Lagrange Polynomials Method. The numerical solution of a linear integral

equations equation is reduced to solving a linear system of algebraic equations. Also, some

numerical examples is presented to show the efficiency of the method.

Keywords: Fredholm integral equations, Lagrange Polynomials, Taylor polynomials. Operational

matrix

References:

[1] L. Bougoffa, R. C. Rach and A. Mennouni, An approximate method for solving a class of weakly-

singular Volterra integro-differential equations. Appl. Math. Comput. 217 (2011), no. 22, 8907--8913.

[2] H. Brunner, On the numerical solution of nonlinear Volterra-Fredholm integral equations by

collocation methods. SIAM J. Numer. Anal. 27 (1990), no. 4, 987--1000.

[3] A. Chakrabarti and A. J. George, A formula for the solution of general Abel integral equation.

Appl. Math. Lett. 7 (1994), no. 2, 87--90.

[4] A. Zerarka *, A. Soukeur, A generalized integral quadratic method: I. an efficient solution for

one-dimensional Volterra integral equation, Communications in Nonlinear Science and Numerical

Simulation 10 (2005) 653–663.

mailto:kfernane@yahoo


42

SOME BOUNDS OF THE FINITE HILBERT TRANSFORM AND

APPLICATIONS IN NUMERICAL INTEGRATION

Fuat USTA

Department of Mathematics, Düzce University, Konuralp Campus, 81620, Düzce, Turkey,

[email protected]

Abstract: The finite Hilbert transform is a useful tool in fields like time series analysis, signal

processing, radar systems, aerodynamics, the theory of elasticity, and other areas of the engineering

sciences. In this study, some explicit bounds and approximations for the finite Hilbert transform are

given for absolutely continuous mappings. Then, some numerical experiments for the obtained

approximation are also presented.

Keywords: Finite Hilbert Transform, Cauchy Principal Value, Numerical Integration.

References:

[1] N. M. Dragomir, S. S. Dragomir, P. M. Farrell and G. W. Baxter, A quadrature rule for the finite

Hilbert transform via trapezoid type inequalities, J. Appl. Math. Comput. 13 (2003), no. 1-2, 6784.

[2] N. M. Dragomir, S.S. Dragomir & P. Farrell, Approximating the finite Hilbert transform via

trapezoid type inequalities, Comput. Math. Appl. 43 (2002), 10-11, 13591369.

[3] W. J. Liu and N. Lu, Approximating the finite Hilbert Transform via Simpson type inequalities

and applications, Politehnica University of Bucharest Scientic Bulletin-Series A-Applied Mathematics

and Physics, 77 (2015), no. 3, 107-122.

[4] W. Liu, X. Gao and Y. Wen, Approximating the finite Hilbert transform via some companions of

Ostrowski’s inequalities. Bull. Malays. Math. Sci. Soc. 39 (2016), no. 4, 1499-1513.

[5] N. Ujevic, A generalization of Ostrowskis inequality and applications in numerical integration,

Appl. Math. Lett., 17 (2004), 133137.

mailto:fuatusta@


43

P-3-PRIME IDEALS IN NEAR RINGS

Funda TAŞDEMİR1, İsmail TAŞTEKİN2

1Department of Mathematics, Yozgat Bozok University, 66100 Yozgat, Turkey,

[email protected]

2Sorgun Türk Telekom Anatolian High School, 66700 Yozgat, Turkey,

[email protected]

Abstract: In this talk, we introduce the notion of P-3-prime ideals, where P is an ideal of a near-ring.

Then, we obtain some relationships between P-3-prime ideal and P-c-prime ideal. It is proved that a

P-c-prime ideal is also a P-3-prime ideal. But the converse holds under some conditions. We provide

examples to illustrate our results.

Keywords: near ring, P-3-prime ideal, P-c-prime ideal.

References:

[1] Pilz, G., Near-rings, 2nd Ed., Amsterdam, New York, Oxford, North-Holland, 1983.

[2] Dheena, P. and Jenila, C., P-Strongly Regular Near-rings, Journal of the Korean Mathematical

Society, 27, 501-506, 2012.



44

ON INCLUSION THEOREMS FOR ABSOLUTE CESÀRO SUMMABILITY

METHODS

G. Canan HAZAR GÜLEÇ1, M. Ali SARIGÖL2

1,2Department of Mathematics, Pamukkale University, Kınıklı Campus, 20070 Denizli, Turkey,

[email protected]

[email protected]

Abstract: In this study, we give necessary and sufficient condition in order that |𝐶, −1|𝑘 ⇒ |𝐶, 𝛼| for

the case 𝛼 > −1 and 𝑘 > 1, so we also complete some open problems in this concept.

Keywords: Sequence spaces, Absolute Cesàro summability, Inclusion relations.

References:

[1] Flett, T.M: On an extension of absolute summability and some theorems of Littlewood and

Paley, Proc. London Math. Soc. 7, 113-141 (1957).

[2] Hardy, G. H: Divergent Series, Oxford, 1949.

[3] Hazar, G. C, Sarıgöl M. A: Compact and Matrix Operators on the Space |𝐶, −1|𝑘, J. Comput.

Anal. Appl., 25(6), 1014-1024 (2018).

[4] Sarıgöl, M.A: Extension of Mazhar's theorem on summability factors, Kuwait J. Sci. 42 (3), 28-

35 (2015).




45

ON THE ZERO POINT PROBLEM OF MONOTONE OPERATORS IN CAT(0)

SPACES

G. Zamani ESKANDANI1, M. RAEISI 2

1,2Department of Pure Mathematics, Faculty of Mathematical Sciences University of Tabriz, Tabriz, Iran,

[email protected]

[email protected]

Abstract: In this paper, a common zero of a finite family of monotone operators and a common

fixed point of an infinitely countable family of quasi-nonexpansive mappings are approximated in

reflexive CAT(0) spaces. In addition, we define a norm on span X* and give an application of this

norm, where X is a CAT(0) space with dual space.

Keywords: Proximal point algorithm, CAT(0) spaces , monotone operator

References:

[1] Espinola, R, Fernandez-Leon, A: CAT(κ)-Spaces, weak convergence and fixed points. J. Math.

Anal. Appl. 353, 410-427 (2009)

[2] M. Bridson and A. Haefliger, Metric Spaces of Non-positive Curvature, Springer-Verlag, Berlin,

Heidelberg, 1999

[3] Kakavandi, B.A., Amini, M.: Duality and subdifferential for convex functions on

complete C A T(0) metric spaces. Nonlinear Anal. 73, 3450–3455 (2010)

[4] Khatibzadeh, H., Ranjbar, S.: Monotone operators and the proximal point algorithm in

complete C A T(0) metric spaces. J. Aust. Math. Soc. 103, 70–90 (2017)

[5] G.Z. Eskandani and M. Raeisi, On the zero point problem of monotone operators in

Hadamard spaces. Numer Algor (2018). https://doi.org/10.1007/s11075-018-0521-3




46

ON MIZOGUCHI-TAKAHASHI'S TYPE SET VALUED

(α-θ) CONTRACTIONS

Gonca DURMAZ1, İshak ALTUN2, Murat OLGUN3 ,Hatice ASLAN HANÇER4

1 Department of Mathematics, Faculty of Science, Çankırı Karatekin Universty, 18100, Çankırı, Turkey,

[email protected]

2,4 Department of Mathematics, Faculty of Science and Art, Kirikkale Universty, Yahşihan, Kirikkale, Turkey

[email protected] , [email protected]

3 Department of Mathematics, Faculty of Science, Ankara Universty, 06100, Tandoğan, Ankara

[email protected]

Abstract: The aim of this talk is to present a new approach to fixed point theorems for multivalued

mappings on complete metric spaces. To do this, we introduce a new concept called MT-type (α-θ)-

contraction and prove fixed point result for such mappings. Also, we present some examples showing

that our result is a real generalization of some existing results.

Keywords: Fixed point, MT-type, complete metric space.

References:

[1] I. Altun, H. A. Hançer and G. Mınak, On a board category of multivalued weakly Picard

operators, Fixed Point Theory, 18(1), 2017, 229-236.

[2] G. Durmaz, Some theorems for a new type of multivalued contractive maps on metric space,

Turkish Journal of Mathematics, 41(4), 2017, 1092-1100.

[3] M. Jleli and B. Samet, A new generalization of the Banach contraction principle, J. Ineq. Appl.,

2014, 2014:38 8 pp.

[4] N. Mizoguchi and W. Takahashi, Fixed point theorems for multivalued mappings on complete

metric space, Journal of Mathematical Analysis and Applications, 141(1998), 177-188.

[5] B. Samet, C. Vetro, and P. Vetro, Fixed point theorems forα-ψ contractive type mappings,

Nonlinear Analysis. Theory, Methods and Applications, 75(4), 2012, 2154–2165.






47

NOVEL CONTOUR SURFACES TO THE (2+1)-DIMENSIONAL DATE–JIMBO–

KASHIWARA–MIWA EQUATION


Department of Computer Engineering, Munzur University, Tunceli, Turkey

[email protected]

Abstract: In this manuscript, improved Bernoulli sub-equation function method based on the

Bernoulli differential method is considered. This method is based on the converting the (2+1)-

dimensional Date–Jimbo–Kashiwara–Miwa equation into ordinary differential equation. Some new

solutions such as complex and exponential are obtained. To better understanding of physical

meanings of model are introduced by plotting two- and three-dimensional surfaces along with contour

simulations. Finally, a conclusion is presented by mentioning important acquisitions founded in this

study.

Keywords: Improved Bernoulli sub-equation function method; (2+1)-dimensional Date–Jimbo–

Kashiwara–Miwa Equation; Complex Exponential function solution.

References:

[1] B. Zheng, “A New Bernoulli Sub-Ode Method For Constructing Traveling Wave Solutions For

Two Nonlinear Equations With Any Order”, U.P.B. Sci. Bull., Series A, 73.3, (2011): 1-10.

[2] X.F. Yang, Z.C. Deng and Y. Wei, “A Riccati-Bernoulli sub-ODE method for nonlinear partial

differential equations and its application”, Advances in Difference Equations, 117, (2015): 1-17.

[3] Y.Q.Yuan, B.Tian, W.R. Sun, J.Chai, L.Liu, “Wronskian and Grammian solutions for a (2+1)-

dimensional Date–Jimbo–Kashiwara–Miwa equation”, Computers & Mathematics with

Applications,74.4,(2017): 873-879.

[4] J.C. Pu, H.C. Hu, “Exact solitary wave solutions for two nonlinear systems, Indian Journal of

Physics”, https://doi.org/10.1007/s12648-018-1267-4

[5] B. Zheng, “Application of A Generalized Bernoulli Sub-ODE Method For Finding Traveling

Solutions of Some Nonlinear Equations”, WSEAS Transactions on Mathematics, 7.11, (2012): 618-

626.

[6] H.M.Baskonus, H.Bulut and D.G.Emir, “Regarding New Complex Analytical Solutions for the

Nonlinear Partial Vakhnenko-Parkes Differential Equation via Bernoulli Sub-Equation Function

Method”, Mathematics Letters, 1.1, (2015): 1-9.

[7] H.M.Baskonus, H.Bulut, “On the Complex Structures of Kundu-Eckhaus Equation via Improved

Bernoulli Sub-Equation Function Method”, Waves in Random and Complex Media, 25.4, (2015): 720-

728.

[8] H.M.Baskonus, H.Bulut, “An Effective Scheme for Solving Some Nonlinear Partial Differential

Equation Arising In Nonlinear Physics”, Open Physics, 13.1, (2015): 280–289.

[9] H.M.Baskonus and H.Bulut, “Exponential Prototype Structures for (2+1)-Dimensional Boiti-

Leon-Pempinelli Systems in Mathematical Physics”, Waves in Random and Complex Media, 26.2,

(2016): 201-208.


https://www.sciencedirect.com/science/journal/08981221


https://www.sciencedirect.com/science/journal/08981221/74/4


48

ON THE ROOTS OF AN EVOLUTION EQUATION


Department of Computer Engineering, Munzur University, Tunceli, Turkey

[email protected]

Abstract: In this paper, we apply Bernoulli sub-equation function method to the model which reads

as ‘S-Integrable’ evolution equation. Complex and exponential functional roots are obtained. Plotting

two- and three-dimensional surfaces along with contour simulations give rise to more sophisticated

information about the model. At the end of the paper, we present a conclusion by giving vital

informations about the surfaces of roots.

Keywords: Bernoulli sub-equation function method; ‘S-Integrable’ evolution equation; Complex,

Exponential roots.

References:

[1] Kundu A. Landau–Lifshitz and higher-order nonlinear systems gauge generated from nonlinear

Schrödinger-type equations. J. Math. Phys. 25, (1984), 3433–3438.

[2] Guangxue Zhang , Lili Zhang , Jinqing Wang , Zuohe Chi , A new model for the acoustic wake

effect in aerosol acoustic agglomeration processes, Applied Mathematical Modelling (2018), doi:

10.1016/j.apm.2018.03.027

[3] Ruiqing Ming, Huiqun He, Qiangfa Hu, A new model for improving the prediction of liquid loading

in horizontal gas wells, Journal of Natural Gas Science & Engineering (2018), doi: 10.1016/

j.jngse.2018.06.003.

[4] Jun Bi, Mingyi Zhang, Wenwu Chen, Jianguo Lu, Yuanming Lai, A new model to determine the

thermal conductivity of fine-grained soils, International Journal of Heat and Mass Transfer 123,

(2018) 407–417.

[5] Chunga K, Toulkeridis T. First evidence of aleo-tsunami deposits of a major historic event in

Ecuador. J. Tsunami Soc. Int. 33, (2014);33:55–69.

[6] X.F. Yang, Z.C. Deng and Y. Wei, “A Riccati-Bernoulli sub-ODE method for nonlinear partial

differential equations and its application”, Advances in Difference Equations, 117, (2015): 1-17.

[7] Y.Q.Yuan, B.Tian, W.R. Sun, J.Chai, L.Liu, “Wronskian and Grammian solutions for a (2+1)-

dimensional Date–Jimbo–Kashiwara–Miwa equation”, Computers & Mathematics with

Applications,74.4,(2017): 873-879.

[8] J.C. Pu, H.C. Hu, “Exact solitary wave solutions for two nonlinear systems, Indian Journal of

Physics”, https://doi.org/10.1007/s12648-018-1267-4

[9] E.Yüce, A.Ö. Tarakçıoğlu, Attitudes of Computer Engineering Department Students towards

ESP Courses Integrated to Foreign Language Courses: Tunceli University Case, Bilim ve Gençlik

Dergisi, 1.1: (2013), 1-12.

[10] E.Yüce, “An investigation into the Relationship between EFL Learners’ Foreign Music Listening

Habits and Foreign Language Classroom Anxiety”, International Journal of Languages’ Education

and Teaching, 6(2), (2018): 471-482.




https://www.sciencedirect.com/science/journal/08981221/74/4

https://doi.org/10.1007/s12648-018-1267-4


49

SOME CARISTI TYPE FIXED POINT THEOREMS ON M-METRIC SPACE

Hakan SAHIN1,3, İshak ALTUN2, Duran TURKOGLU3, Hatice ASLAN HANCER2

1Department of Mathematics, Amasya University, Faculty of Science, Amasya, Turkey

[email protected]

2Department of Mathematics, Kırıkkale University, Faculty of Science, Kırıkkale, Turkey,

[email protected], [email protected]

3Department of Mathematics, Gazi University, Faculty of Science, Ankara, Turkey,

[email protected]

Abstract: Recently, concept of M-metric which is extension of partial metric and usual metric is

defined by Asadi et al. In this paper, we prove caristi type fixed point theorem and then, we give

some generalizations of caristi type fixed point theorem on M-metric space. Finally, we support our

idea with nontrivial examples.

Keywords: fixed point, caristi type, M-metric

References:

[1] Asadi, M, Karapınar, E, and Salimi, P: New extension of p-metric spaces with some fixed point

results on M-metric spaces. Journal of Inequalities and Applications, 2014 (2014): 18

[2] Caristi, J: Fixed point theorems for mapping satisfying inwardness conditions. Trans. Amer.

Math. Soc. 215, 241-251 (1976)

[3] Bae, J. S: Fixed point theorems for weakly contractive multvalued maps. J. Math. Anal. App. 28,

690-697 (2003)

[4] Suzuki, T: Generalized Caristi’s fixed point theorems by Bae and others. J. Math. Anal. App.

302, 502-508 (2005)





50

QUASI-HAUSDORFF TRANSFORMATIONS FOR DOUBLE SEQUENCES

Hamdullah ŞEVLİ

İstanbul Ticaret University

Abstract: Quasi-Hausdorff transformations for single sequences were defined by Hardy [1]. The aim

of this presentation is to extend to double sequences some of the results which have been proved

for Quasi-Hausdorff matrices.

Keywords: Quasi-Hausdorff matrices, double series, absolute summability.

AMS 2010. 40F05, 40G05.

References:

[1] Hardy, G.H., Divergent series, Clarendon Press, Oxford, 1949.


51

WEIGHTED COMPOSITION OPERATORS FROM BLOCH-TYPE SPACES

INTO BERS-TYPE SPACES

Hamid VAEZI1, Mohamad NAGHLISAR2

1,2Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran,

[email protected]

[email protected]

Abstract: In this paper we consider the weighted composition operator from Bloch-type space 𝐵𝛼

into Bers-type space 𝐻𝛽∞ in three cases, α >1 , α =1 and α <1. We give necessary and sufficient

conditions for boundedness and compactness of the above operator.

Keywords: Weighted composition operator, Bloch-type space, Bers-type

space, Boundedness, Compactness.

References:

[1] Colonna F. and Li S., Weighted composition operator from the Besov spaces to the Bloch

spaces, Bull. Malaysian Sci. Soc., 36(4) (2013),1027-1039.

[2] Cowen C. C. and Maccluer B. D., Composition operators on spaces of analytic functions,

Studies in Advanced Math., CRC Press, Boca Raton (1995).

[3] Hassanlou, M., Vaezi H. and Wang M., Weighted composition operators on weak vector-valued

Bergman spaces and Hardy spaces, Banach J. Math. Anal., 9(2) (2015), 35-43.

[4] Weixian H. and Lijian j., Composition operator on Bers-type spaces, Acta. Math. Sci., 22B(3)

(2002), 404-412.

mailto:[email protected]@gmail.com


52

ON SEMICOMMUTATIVE RINGS

Handan KOSE

Kırşehir Ahi Evran University, Department of Mathematics, Kırşehir

[email protected]

Abstract: A ring 𝑅 is called semicommutative if for any 𝑎, 𝑏 ∈ 𝑅, 𝑎𝑏 = 0 implies 𝑎𝑅𝑏 = 0. The ring 𝑅

is semicommutative if and only if any right (left) annihilator over 𝑅 is an ideal of 𝑅 by [1, Lemma 1] or

[2, Lemma 1.2]. A ring 𝑅 is called nil-semicommutative [3] if 𝑎𝑏 = 0 implies 𝑎𝑅𝑏 = 0 for every nilpotent

elements 𝑎, 𝑏 ∈ 𝑅. Another version of semicommutativity is weak semicommutativity. The ring 𝑅 is

called weakly semicommutative if for any 𝑎, 𝑏 ∈ 𝑅, 𝑎𝑏 = 0 implies 𝑎𝑟𝑏 is nilpotent for any 𝑟 ∈ 𝑅.

In this work, we study some cases when an amalgamated construction 𝐴 ⋈𝑓 𝐼 ≔ {(𝑎, 𝑓(𝑎) + 𝑖): 𝑎 ∈

𝐴, 𝑖 ∈ 𝐼} of a ring 𝐴 along an ideal 𝐼 of a ring 𝐵 with respect to a ring homomorphism 𝑓 from 𝐴 to 𝐵,

is semicommutative, nil-semicommutative and weakly semicommutative.

Keywords: Semicommutative ring, nil-semicommutative ring and weakly semicommutative ring.

Acknowledgement: This work was supported by the Ahi Evran University Scientific Research

Projects Coordination Unit. Project Number: FEF. A4. 18. 008

References:

[1] C. Huh, Y. Lee, A. Smoktunowicz, Armendariz rings and semicommutative rings, Comm. Algebra,

2002, 30(2), 751-761.

[2] G. Shin, Prime ideals and sheaf representations of a pseudo symmetric ring, Trans. Amer. Math.

Soc., 1973, 184, 43-60.

[3] R. Mohammadi, A. Moussavi, M. Zahiri, On nil-semicommutative rings, Int. Electron. J. Algebra,

2012, 11, 20-37.



53

SOME OPERATOR INEQUALITIES

Havva TİLKİ1, Mualla Birgül HUBAN2, Mehmet GÜRDAL3

1Department of Mathematics, Süleyman Demirel University, East Campus, 32100 Isparta, Turkey,

[email protected]

2 Department of Mathematical Engineering, Süleyman Demirel University, East Campus, 32100 Isparta,

Turkey,

[email protected]

3 Department of Mathematical Engineering, Süleyman Demirel University, East Campus, 32100 Isparta,

Turkey,

[email protected]

Abstract: In this paper, we will use some known operator inequalities for proving some new

inequalities for the Berezin number of operators acting on the reproducing kernel Hilbert spaces.

Keywords: Reproducing kernel Hilbert space, Berezin symbol, Berezin number, quasi-paranormal

operator, Hölder-McCarthy type inequality, Young type inequality.

References:

[1] Aronszajn, N., Theory of Reproducing Kernel. Trans American Mathematical Society, 68 (1950),

337-404.

[2] Karaev, M.T., Gürdal, M., Huban, M.B., Reproducing kernels, Engliš algebras and some

applications. Studia Mathematica, 232(2) (2016), 113-141.

[3] Karaev, M.T., Gürdal, Okudan, A., Hardy-Hilbert inequality and Power inequalities for Berezin

numbers of operators, Math. Inequal. Appl., 19(3), (2016) 883-891.





54

EPI EULER CONVERGENCE OF KIND CONVERGENT SETS

Harun POLAT

Muş Alparslan University Art and Science Faculty, Department of Mathematics, 49100 Muş,Turkey.

[email protected]

Abstract: There are different convergence notions for sequence of sets, which have significance for

certain applications. Kuratowski convergence, Hausdorff convergence, Wijsman convergence,

Fisher convergence and Mosco convergence are the best known types of convergence. In this paper

we peresent definitions Epi EulerConvergence of Kuratowski convergence, Epi Euler Convergence

of Hausdorff convergence, Epi Euler Convergence of Wijsman convergence, Epi Euler Convergence

of Fisher convergence and Epi Euler Convergence of Mosco convergence of sequences of sets. Also

we characterize the connection between of their.

Keywords: Epi Euler convergence, Kuratowski, Hausdorff, Wijsman, Fisher and Mosco

convergence.

References:

[1] C. Kuratowski, Topology, Academic Press, New York, 1966.

[2] F. Hausdorff , Grundzuge derMengenlehre, Verlag von Veit, Leipzig, Reprinted by Chelsea, New

York1914.

[3] R. A. Wijsman,” Convergence of sequences of convex sets, cones and functions”, Bull. Amer.

Math. Soc. 70 (1964) 186-188.

[4] B. Fisher, “Common fixed points of mappings and set-valued mappings”, Rostock Math. Kolloq.

18 (1981) 69-77.

[5] U. Mosco, “Convergence of convex sets and of solutions of variational inequalities”, Adv. in Math.

3 (1969), 510--585.


55

NEW TOPOLOGY IN 𝜷(𝑰)

Hassan MOUADI1, Driss KARIM2

1Faculty of Sciences and Techniques , University HASSAN 2, Mohammedia, Morocco.

[email protected]

2 Department of Mathematics, Faculty of Sciences and Techniques , University HASSAN 2, Mohammedia,

Morocco.

[email protected]

Abstract: In this study, we give definition of F-topology in β(I) set of all ultrafilter in I and give some

propriety of maximal and prime ideals of product of infinity rings (I is the index set)

Keywords: ultrafilter , nilpotent index, F-lim, F-topology.

References:

[1] M.F. Atiyah and I.G. Macdonald, Introduction to commutative algebra, Addison-Wesley, 1969

[2] M. Fontana and K. A. Loper, The patch topology and the ultrafilter topology on the prime

spectrum of a commutative ring, Comm. Algebra 36(2008), 2917-2922

[3] Jay. Shapiro, The Prime Spectrum of an Infinite Product of Zero-Dimensional Rings, Zero-

Dimensional Commutative Rings, 1995

[4] S. Garcia-Ferreira and L. M. Ruza-Montilla, The F-lim of a Sequence of Prime Ideals,

Communications in Algebra 39(7):2532-2544 _ July 2011

[5] L.Gillman and M. Heinzer, Product of commutative rings and zero dimensionality,Trans. Amer.

Math. Soc.,331 (1992), 663-680.




56

INVESTIGATION OF SUBORBİTAL GRAPHS OF THE

TYPE

𝜞𝟎(𝑳, 𝑴) = (𝒂 𝒃𝑴

𝒄𝑳 𝒅)

İbrahim GÖKCAN

Department of Mathematics, Institute of Science and Technology,Karadeniz Technical University, Trabzon,

Turkey,

[email protected]

Abstract: In this study, the definition of suborbital graphs of the type 𝛤0(𝐿, 𝑀) = (𝑎 𝑏𝑀𝑐𝐿 𝑑

), its

transitive and invariant state on the set of generalized rational numbers, basic congruence groups,

number of basic congruence groups and some of its other features have been tried to be examined

with the help of definitions and theories of basic graph theories. 𝛤0(n) ≔ {(𝑎 𝑏𝑐 𝑑

) ∈ Γ|𝑐 ≡

0 mod n } is connected to the congruential basis 𝑛 and 𝛤0(𝐿, 𝑀) = {( 𝑎 𝑏𝑀𝑐𝐿 𝑑

) ∈ 𝛤|𝑎, 𝑏, 𝑐, 𝑑 ∈

ℤ ve 𝑎𝑑 − 𝑏𝑐(𝐿𝑀) = 1 } is connected to 𝐿. Furthermore, it has been shown that 𝛤0(𝐿, 𝑀) moves

on ℚ̂ in an imprimitive way, thus, by defining the G-invariant equivalence relation, a different equation

relation on 𝛤0(𝐿, 𝑀) is defined which is different from universal and identity equivalence relations.

Keywords: Suborbital Graphs, Basic Congruence Groups, Transitive and Invariant.

References:

[1] Akbaş, M., On Suborbital Graphs for Modular Group, Bull. London Math. Soc., 33 (2011), 647-

652.

[2] Jones, G.A., Singerman, D. Ve Wicks, K., The Modular Group and Generalized Farey Graphs,

London Math. Soc. Lecture Notes, CUP, Cambridge, 160 (1991) 316-338.

[3] Ünal, H., Alt Yörüngesel Graflar ve Fibonacci Sayıları, Yüksek Lisans Tezi, K.T.Ü, Fen Bilimleri

Enstitüsü, Trabzon, 2013.



57

WEIGHTED STOCHASTIC FIELD EXPONENT LEBESGUE AND SOBOLEV

SPACES

Ismail AYDIN1, Cihan UNAL2

1,2Department of Mathematics, Sinop University, Sinop, Turkey,

[email protected]

[email protected]

Abstract: In this study, we introduce weighted stochastic field exponent Lebesgue and Sobolev

spaces. After discussing some basic properties and embeddings of these spaces, we will want to

show an application of these spaces to the stochastic partial differential equations with stochastic

field growth.

Keywords: Weighted stochastic field exponent Lebesgue and Sobolev spaces, compact

embedding, weak solution, stochastic partial differential equation.

References:

[1] I. Aydın, Weighted Variable Sobolev Spaces and Capacity, Journal of Function Spaces and

Applications, Vol. 2012, Article ID 132690, (2012): 17 pages, doi:10.1155/2012/132690.

[2] B. Lahmi, E. Azroul and K. El Haiti, Nonlinear Degenerated Elliptic Problems with Dual Data and

Nonstandard Growth, Math. Reports, 20 (70). 1 (2018): 81-91.

[3] B. Tian, B. Xu and Y. Fu, Stochastic Field Exponent Function Spaces with Applications,

Complex Variables and Elliptic Equations, 59. 1 (2014): 133-148.

[4] C. Unal and I. Aydın, Weighted Variable Exponent Sobolev Spaces with Zero Boundary Values

and Capacity Estimates, Sigma J Eng & Nat Sci 36 (2), (2018): 371-386.




58

SOME COMPACTNESS CRITERIONS IN WEIGHTED VARIABLE EXPONENT

AMALGAM SPACES

Ismail AYDIN1, Cihan UNAL2

1,2Faculty of Arts and Sciences, Department of Mathematics, Sinop University,

57000 Sinop, Turkey,

[email protected]

[email protected]

Abstract: In this study, we consider totally bounded subsets in weighted variable exponent amalgam

and Sobolev spaces. Moreover, we present some new conditions and criterions for compactness of

bounded subsets in these spaces.

Keywords: Weighted amalgam and Sobolev spaces, compactness, totally bounded sets

References:

[1] I. Aydın, On vector-valued classical and variable exponent amalgam spaces, Commun. Fac.

Sci. Univ. Ank. Series A1, 66(2), 100-114 (2017)

[2] R. Bandaliyev, Compactness criteria in weighted variable Lebesgue spaces, Miskolc Math.

Notes, 18(1), 95-101 (2017)

[3] P. Gorka, A. Macios, Almost everything you need to know about relatively compact sets in

variable Lebesgue spaces, J. Funct. Anal., 269(7), 1925-1949 (2015)

[4] H. Hanche-Olsen, H. Holden, The Kolmogorov-Riesz compactness theorem, Expo. Math.,

28(4), 385-394 (2010)

[5] A. N. Kolmogorov, Über Kompaktheit der Funktionenmengen bei der Konvergenz im Mittel,

Nachr. Ges. Wiss. Göttingen, 9, 60-63 (1931).




59

CONVERGENCE ANALYSIS OF A NEW MODIFIED JUNGCK-THREE-STEP

ITERATIVE METHOD IN THE BANACH SPACES

Kadri DOĞAN1, Yılmaz ALTUN2

1Department of Computer Engineering , Artvin Coruh University, Artvin/Turkey

[email protected]

2 Department of Mathematics, Ahi Evran University, Kırşehir, Turkey,

yı[email protected]

Abstract: In this study, Some strong convergence results for modified Jungck-three-step iterative

scheme has been established in a Banach space. Comparison of this modified iteration scheme with

Jungck-three iterative scheme has been made by solving some scalar nonlinear equations.

Keywords: Jungck-type iterative process, Banach space, fixed point, strong convergence.

References:

[1] G. Jungck, Commuting Mappings and Fixed Points, Amer. Math. Monthly 83, No. 4 (1976) 261-

263.

[2] S. L. Singh, C. Bhatnagar and S. N. Mishra, Stability of Jungck-Type Iterative Procedures,

Internatioal J. Math. & Math. Sc. 19, (2005) 3035-3043.

[3] M. O. Olatiwo and C. O. Imor, Some Convergence results for the Jungck Mann and the Jungck

Ishikawa iteration process in the class of generalized zamfirescue operators,Acta Math. Univ.

Comenianae Vol. LXXVII, 2, (2008) 299-304.




60

CONVERGENCE ANALYSIS OF JUNGCK-MP ITERATIVE METHOD IN THE

BANACH SPACES

Kadri DOĞAN1, Vatan KARAKAYA2

1Department of Computer Engineering , Artvin Coruh University, Artvin/Turkey

E-mail: [email protected]


Istanbul,Turkey,

[email protected]

Abstract: In this study, Some strong convergence results for modified Jungck-MP iteration schemes

have been established in a Banach space. Comparison of this modified iteration scheme with Jungck-

Ishikawa iteration scheme has been made by solving some scalar nonlinear equations.

Keywords: Jungck-MP iterative process, Banach space, fixed point, strong convergence. References: [1] G. Jungck, Commuting Mappings and Fixed Points, Amer. Math. Monthly 83, No. 4 (1976) 261-263 [2] S. L. Singh, C. Bhatnagar and S. N. Mishra, Stability of Jungck-Type Iterative Procedures, Internatioal J. Math. & Math. Sc. 19, (2005) 3035-3043.

[3] M. O. Olatiwo and C. O. Imor, Some Convergence results for the Jungck Mann and the Jungck Ishikawa iteration process in the class of generalized zamfirescue operators,Acta Math. Univ. Comenianae Vol. LXXVII, 2, (2008) 299-304.




61

FIXED POINT THEOREMS VIA SIMULATION TYPE FUNCTIONS

Merve İLKHAN

Department of Mathematics, Düzce University, Düzce, Turkey,

[email protected]

Abstract: The main goal of this study is to establish some results for the existence and uniqueness

of fixed points by the aid of simulation functions in the setting of generalized metric spaces.

Keywords: fixed point theorems, simulation functions, complete spaces.

References:

[1] S. Banach, “Sur les opérations dans les ensembles abstraits et leur application aux équations

integrals”, Fund. Math. 3 (1922) 133-181.

[2] F. Khojasteh, S. Shukla and S. Radenovic, “A new approach to the study of fixed point theorems via simulation functions”, Filomat 96 (2015) 1189-1194.

[3] A. Roldan-Lopez-de-Hierro, E. Karapinar , C. Roldan-Lopez-de-Hierro and J. Martinez

Morenoa, “Coincidence point theorems on metric spaces via simulation function”, J. Comput. Appl.

Math. 275 (2015) 345–355.

[4] C. Mongkolkeha, , Y. J. Cho and Poom Kumam, ” Fixed point theorems for simulation functions

in b-metric spaces via the wt-distance”, Appl. Gen. Topol. 18(1) (2017) 91-105.



62

Δ - CONVERGENCE AND STRONG CONVERGENCE IN GENERALIZED CAT

(0) SPACES

Mohammad KNEFATI1 and Vatan KARAKAYA2

1Yildiz Technical University,Istanbul TURKEY

[email protected]

2Department of Mathematical Engineering, Yildiz Technical University, Davutpasa Campus, Esenler, 34210

Istanbul,Turkey,

[email protected]

Abstract: We establish strong and Δ - convergence for some iteration schames in generalized CAT

(0) spaces which is introduced by Khamsi [7].

References:

[1] M.A.Khamsi and S.Shukri,Generalized CAT(0) spaces.

[2] H.Fukharuddin and M.A.Khamsi,approximating common fıxed points in hyperbolic spaces.




63

ON I2-CAUCHY DOUBLE SEQUENCES IN FUZZY NORMED SPACE

Muhammed Recai TÜRKMEN1, Erdinç DÜNDAR2

1Department of Mathematics, Faculty of Education, AfyonKocatepe University, 03200, Afyonkarahisar, Turkey,

[email protected]

2 Department of Mathematics, Faculty of Science and Literature, Afyon Kocatepe University, 03200,

Afyonkarahisar,Turkey,

[email protected]

Abstract: In this study, we have investigated the concepts of I2-Cauchy and I2-convergence of

double sequences in fuzzy normed spaces. Also, we have investigated some properties and

relationships between these concepts.

Keywords: Double sequences, 2I convergence,

2I Cauchy,, Fuzzy normed spaces.

References:

[1] P. Das, P. Kostyrko, W. Wilczynski, P. Malik, I and I*-convergence of double sequences,

Math.Slovaca 58 (5) (2008), 605-620.

[2] E. Dündar, B. Altay, I2-convergence and I2-Cauchy of double sequences, Acta Mathematica

Scientia, 34(2) (2014), 343-353.

[3] E. Dündar, Ö. Talo, I2-convergence of double sequences of fuzzy numbers, Iranian Journal of

Fuzzy Systems Vol. 10, No. 3, (2013) pp. 37-50.

[4] E. Dündar, Ö. Talo, I2-Cauchy Double Sequences of Fuzzy Numbers, Gen. Math. Notes, 16(2)

(2013), 103-114.

[5] V. Kumar, On I and I*-convergence of double sequences, Math. Commun. 12 (2007), 171-181.

[6] V. Kumar, K. Kumar, On the ideal convergence of sequences of fuzzy numbers, Inform. Sci.,178

(2008), 4670-4678.

[7] M. R. Türkmen and M. Çınar, Lambda Statistical Convergence in Fuzzy Normed Linear Spaces,

Journal of Intelligent and Fuzzy Systems, 34 (6) (2018), 4023-4030

[8] L.A. Zadeh, Fuzzy sets, Information and Control 8(1965), 338-353.




64

LACUNARY STATISTICAL CONVERGENCE IN FUZZY N-NORMED LINEAR

SPACES


Department of Mathematics, Faculty of Education, AfyonKocatepe University, 03200 Afyonkarahisar, Turkey,

[email protected]

Abstract: In this paper, we introduced the concept of lacunary statistical summable and lacunary

statistical convergence in fuzzy n-normed linear spaces. It also has studied the some properties

these concepts.

Keywords: Lacunary convergence, Statistical convergence, Lacunary summable, Fuzzy n-normed

space.

References:

[1] H. Altınok, Y. Altın, and M. Et, Lacunary almost statistical convergence of fuzzy numbers, Thai

Journal of Mathematics, 2 (2) (2004), 265–274.

[2] J. A. Fridy and C. Orhan, Lacunary Statistical Convergence, Pasific Journal of Mathematics,

160 (1) (1993), 43–51.

[3] F. Nuray, Lacunary statistical convergence of sequences of fuzzy numbers, Fuzzy Sets

Systems, 99 (1998), 353–355.

[4] F. Nuray, U. Ulusu, and E. Dündar, Lacunary statistical convergence of double sequences of

sets, Soft Computing, 20 (7) (2016), 2883–2888.

[5] M. R. Türkmen and M. Çınar, Lacunary Statistical Convergence in Fuzzy Normed Linear

Spaces, Applied and Computational Mathematics, 6 (5) (2017), 233–237.

[6] M. R. Türkmen and H. Efe, On Some Properties Of Closability Of Farthest Point Maps in Fuzzy

n-Normed Spaces, imanager’s Journal on Mathematics, 2 (4) (2013), 33–38.

[7] M. R. Türkmen and E. Dündar, On lacunary statistical convergence of double sequences and

some properties in fuzzy normed spaces, Journal of Intelligent and Fuzzy Systems, DOI:10.

3233/JIFS-18841.




65

SOME RESULTS ON 𝝀 − STATISTICAL CONVERGENCE OF DOUBLE

SEQUENCES IN FUZZY NORMED SPACE


Department of Mathematics, Faculty of Education, AfyonKocatepe University, 03200 Afyonkarahisar, Turkey,

[email protected]

Abstract: In this paper, we have introduced statistical convergence and condition of being

statistical Cauchy for double sequences in fuzzy normed linear spaces and we have studied some

results these concepts.

Keywords : Double sequences, Statistical convergence, statistical convergence, Fuzzy

normed space.

References:

[1] R. Çolak, On statistical convergence, Conference on Summability and Applications, May

12-13, (2011), Istanbul Turkey.

[2] M. Et ; M. Çınar and M. Karakaş, On statistical convergence of order of sequences of

function, J. Inequal. Appl., 204 (2013), 1-8.

[3] M. Mursaleen, statistical convergence, Math. Slovaca, 50(1) (2000), 111-115.

[4] E. Savas, On Strongly summable Sequences of Fuzzy Numbers, Information Science,

125(1-4) (2000), 181-186.

[5] F. Nuray, E. Savaş, Statistical convergence of sequences of fuzzy numbers, Math. Slovaca,

45(3) (1995), 269–273.



[7] M. R. Türkmen and M. Çınar, Lambda Statistical Convergence in Fuzzy Normed Linear Spaces,

Journal of Intelligent and Fuzzy Systems, 34 (6) (2018), 4023-4030




66

LACUNARY I-CONVERGENCE IN FUZZY NORMED SPACES


Department of Mathematics, Faculty of Education, Afyon Kocatepe University, 03200 Afyonkarahisar, Turkey,

[email protected]

Abstract: In this paper, we have introduced lacunary ideal convergence and condition of being

lacunary ideal Cauchy in fuzzy normed linear spaces and study some properties and relations of

these concepts.

Keywords: Lacunary Convergence, Statistical convergence, I-convergence, Fuzzy n-normed

space

References:

[1] H. Altınok, Y. Altın, and M. Et, Lacunary almost statistical convergence of fuzzy numbers, Thai

Journal of Mathematics, 2 (2) (2004), 265–274.

[2] J. A. Fridy and C. Orhan, Lacunary Statistical Convergence, Pasific Journal of Mathematics,

160 (1) (1993), 43–51.

[3] F. Nuray, Lacunary statistical convergence of sequences of fuzzy numbers, Fuzzy Sets

Systems, 99 (1998), 353–355.

[4] F. Nuray, U. Ulusu, and E. Dündar, Lacunary statistical convergence of double sequences of

sets, Soft Computing, 20 (7) (2016), 2883–2888.



[6] M. R. Türkmen and H. Efe, On Some Properties Of Closability Of Farthest Point Maps in Fuzzy

n-Normed Spaces, imanager’s Journal on Mathematics, 2 (4) (2013), 33–38.

[7] M. R. Türkmen and E. Dündar, On lacunary statistical convergence of double sequences and

some properties in fuzzy normed spaces, Journal of Intelligent and Fuzzy Systems, DOI:10.

3233/JIFS-18841.




67

NEW TYPE SOFT SET AND MEDICAL DECION MAKING APPLICATION

Murat KİRİŞCİ

Department of Mathematical Education, Istanbul University-Cerrahpaşa, Fatih, 34470 Istanbul, Turkey,

[email protected]

Abstract: In this study we apply new soft set theory for medical decion making. The problem is to

choose patient people with the variables used for Type II Diabetes Mellitus diagnosis. A comparison

matrix will be obtained for this selection and the maximum score will be reached with this matrix.

Keywords: soft set theory, decision making, comparison matrix.

References:

[1] M. Kirişci, H. Yılmaz, M. U. Saka, “An ANFIS perspective for the diagnosis of Type II Diabetes”,

(under communication)

[2] D. Molodtsov. " Soft Set Theory-First Results", Comput. Math. Appl. 37, (1999): 19-31.

[3] L.A: Zadeh. "Fuzzy Sets" Inf. Comp. 8, (1965): 338-353.



68

REASONABLE MODIFICATIONS UNDER THE B-SPLINE BASIS WITH THE

SSPRK54 FOR SOLVING THE BURGERS EQUATION

Murat SARI, S. Ali-TAHIR

Yildiz Technical University, Department of Mathematics, Faculty of Arts and Science, 34220, Istanbul, Turkey,

[email protected]

[email protected]

Abstract: In this work, we develop here a striking numerical method for solving the Burgers

equation. The numerical scheme is based on collocation of the modified cubic B-splines in the space

variable. The obtained results have been computed without using any linearization and

transformation processes. The produced diagonal system is solved by using the optimal strong

stability preserving time stepping Runge-Kutta for five stage and order four scheme (SSPRK54). The

present method is seen to be approximate for the advection dominant cases. The effectiveness of

this method is verified by considering some test problems for different values of the viscosity that can

be caused by the steep shock behavior. The numerical solutions are in good agreement with the

exact solutions and competent with those available in the literature. The present method is seen to

be relatively easy and economical implementation for researchers.

Keywords: cubic B-spline basis; Burgers equation; SSPRK54 method; CFL condition.

References:

[1] Boor C., A Practical Guide to Spline, Mathematics of Computation, 27, (1978).

[2] Schumaker L., Spline Functions, Basic Theory, Cambridge Mathematical Library, (2007)

[3] Schoenberg I. J., Contribution to the problem of approximation of equidistant data by analytic

functions, Quart. Appl.Math., 45-99, (1946)

[4] Morton K.W. and Mayers D.F., Numerical Solution of Partial Differential Equations?,

Cambridge university press, (1994)

[5] Mittal R.C.,Jain R.K., Numerical solution of nonlinear burgers equation with modified cubic B-

spline collocation method, Appl, math, comput, 218, 7839-7855, (2012)

[6] Dag I., irk D., Sahin A., B-Spline collocation methods for numerical solutions of the Burgers

equation, Math, Prob, 5, 521-538, (2005)

[7] Sari M., Gurarslan G. Numerical solutions of the generalized Burgers-Huxley equation by a

differential quadrature method. Mathematical 11: 370-765 (2009).




69

NEW JUNGCK-TYPE ITERATIVE ALGORITHM AND NUMERICAL

RECKONING COINCIDENCE POINTS IN CONVEX METRIC SPACES

Musa DİKMEN1, Faik GÜRSOY2

1,2Department of Mathematics, Adiyaman University,02040 Adiyaman, Turkey,

[email protected]

[email protected]

Abstract: In this presentation, we introduce a new Jungck-type iterative algorithm for a general class

of mappings and study its qualitative features like strong convergence, rate of convergence, stability

in convex metric spaces and data dependency in hyperbolic spaces. Validity of theoretical findings

obtained herein is shown through numerical examples. Our results are improvements and

generalizations of some recent results in the current literature.

Keywords: Almost contraction mappings, Jungck-type iterative algorithm, strong convergence, rate

of convergence, stability, data dependency.

References:

[1] Karakaya, V, Atalan, Y, Doğan, K, El Houda Bouzara, N, Some fixed point results for a new

three steps iteration process in Banach spaces, Fixed Point Theory 18, 625-640 (2017).

[2] F. Gürsoy, A. R. Khan, H. Fukhar-ud-din, Convergence and data dependence results for quasi-

contractive type operators in hyperbolic spaces, Hacet. J. Math. Stat. 46, 391-406 (2017).




70

SOME FIXED POINT THEOREMS IN CONE METRIC SPACES OVER BANACH

ALGEBRAS

Muttalip ÖZAVŞAR

Department of Mathematics, Yildiz Technical University, Istanbul, Turkey

[email protected]

Abstract: After Banach[1] introduced the contraction mapping principle in 1922, many researchers

extended his result to different contractive type mappings in the usual metric spaces and some

abstract spaces. For example, in 1989, Bakhtin [2] introduced b-metric space and then in 1993,

Czerwik [3] extended Banach’s principle to b-metric spaces. At the beginning of the 21 st century,

Berinde[4] presented the notion of (k,l)-almost contractions, which contains the classes of many

mappings such as Banach, Kannan and Chatterja type contractive mappings. Recently, Liu and Xu

[5] studied Banach’s contraction principle by using tools of spectral radius in the setting of cone metric

spaces over Banach algebra with a solid normal cone. Later, Xu and Radenovic [6] obtained the

results of [5] by omitting the normality condition for solid in underlying Banach algebra. In [7], the

fixed point theorem for (k,l)-almost contraction mappings is presented in the setting of cone metric

spaces over Banach algebras. In [8], Huang and Radenovic introduce some fixed point theorems

by introducing the notion of cone b-metric spaces over Banach algebras. In [9], George, Nabwey,

Rajagopalan, Radenovic and Reshma define the notion of cone b-metric with vector coefficient in

the setting of Banach algebra. In this talk we present the fixed point theorem for (k,l)-almost

contaction mappings in the setting of cone b-metric spaces with vector coefficient over Banach

Algebras.

References:

[1] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations

integrales, Fundamenta Mathematicae 3 (1922), 133–181.

[2] I. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal. Unianowsk,

Gos. Ped. Inst. 30 (1989), 26–37.

[3] S. Czerwick, Contraction mappings in b-metric spaces, Acta Mathematica et Informatica

Universitatis Ostraviensis 1 (1993), 5–11.

[4] V. Berinde, Approximating fixed points of weak contractions using the Picard iterations. Nonlinear

Anal. Forum. 9(2004), 43-53.

[5] H. Liu and S. Xu, Cone metric spaces with Banach algebras and fixed point theorems of

generalized Lipschitz mappings, Fix P Theory Appl. (2013), 10 pages.

[6] S. Xu and S. Radenovic, Fixed point theorems of generalized Lipschitz mappings on cone metric

spaces over Banach algebras without assumption of normality, Fix. P. Theory Appl. (2014), 12

pages.

[7] M.Özavşar, Fixed point theorems for (k,l)-almost contractions in cone metric spaces over Banach

algebras, Math.Adv.Pur.Appl.Sci. 1(2018), 46-51.



71

ON FINITE DIMENSIONAL LEIBNIZ ALGEBRAS

Mücahit ÖZKAYA1, Nil MANSUROĞLU2


[email protected]

[email protected]

Abstract: In literature, firstly Leibniz algebras which are generalization of Lie algebras were

introduced as D-algebras by A.M. Bloh. Then, in 1993 these algebras which are called Leibniz

algebras were rediscovered by J.L. Loday. There are many researches on finite dimensional Leibniz

algebras. In this note, our main aim is to focus on finite dimensional Leibniz algebras and to give

some properties for the structure constants of Leibniz algebras.

Keywords: Lie algebra, Leibniz algebra, dimension, structure constant.

This work was supported by Kırşehir Ahi Evran University Scientific Research Projects Coordination

Unit. Project Number: FEF.A4.18.009.

References:

[1] Bloh, A.M. A generalization of the concept of Lie algebras, Dokl. Nauk. SSR, 165, 471-473

(1965)

[2] Demir, İ.; Kailash, C.M.; Stitzinger, E. On some structures of Leibniz algebras,

arXiv:1307.7672v1.

[3] Jacobson, N. Lie algebras, Dover, (1979)

[4] Loday, J.L. Une version non commutative des algebres de Lie: les algebres de Leibniz,

L'Enseignement Mathématique, 39, 269-293, (1993).




72

CONVERGENCE AND STABILITY RESULTS FOR K* ITERATION

Müzeyyen ERTÜRK1, Faik GÜRSOY2, Vatan KARAKAYA3

1,2Department of Mathematics, Adıyaman University, 02040 Adıyaman, Turkey,

[email protected],

[email protected]


Istanbul,Turkey,

[email protected]

Abstract: In this presentation, we study convergence and stability results for K* iteration defined by

Ullah and Arshad [1] for a class mapping which includes the contractions. Also, we support our results

with the illustrative examples.

Keywords: K* iteration, convergence, stability

References:

[1] Ullah, K., and Arshad, M.: New three-step iteration process and fixed point approximation in

Banach spaces. Journal of Linear and Topological Algebra, 7.2, 87-100 (2018).




73

A STUDY ON LATERAL BASES AND COVERED LATERAL IDEALS OF

ORDERED TERNARY SEMİGROUPS

M. Yahya ABBASI, Sabahat Ali KHAN and Aakif Fairooze TALEE

Department of Mathematics, Jamia Millia Islamia, New Delhi-110 025, India

[email protected]

Abstract: In this paper, we define lateral bases and covered lateral ideals of ordered ternary

semigroups. Here we study their related properties and explore the relationship between lateral

base and covered lateral ideal of an ordered ternary semigroup.

Keywords: Ordered ternary semigroups, Lateral bases, Covered lateral ideals.

MSC(2010): 020M12, 20N99.



74

APPROXIMATION PROPERTIES OF THE BERNSTEIN-CHLODOWSKY-

DURRMEYER OPERATORS ON THE WHOLE REEL AXIS

Nadire Fulda ODABAŞI1, Aydın İZGİ2

1,2Department of Mathematics, Harran University, Osmanbey Campus, Şanlıurfa, Turkey,

[email protected]

[email protected]

Abstract: In this study, we introduced the Bernstein-Chlodowsky-Durrmeyer operators and

investigated some approximation properties of these operators. We obtained Korovkin type

approximation properties of these operators and estimated their rate of convergence by modulus of

continuity.

Keywords: Bernstein-Chlodowsky-Durrmeyer type operators, rate of convergence, modulus of

continuity.

References:

[1] Bernstein, S. N: Demonstration du theorem de Weierstrass fondee sur le calculu des

probabilites. Comp. Comm. Soc. Mat. Charkow. Ser., 13(2), 1-2 (1912).

[2] Chlodowsky, I: Sur le developpement des fonctions definies dans un intervalle infini en series

de polynomes de M. S. Bernstein. Compositio Math., 4, 380-393 (1937).

[3] Durrmeyer, J. L: Une formule d’inversion de la transformee de Laplace: applications a la

theorie des moments. These de 3e Cycle, Faculte des Sciences de I’Universite de Paris, 1967.




75

ON 𝝀 𝝂-STATISTICAL CONVERGENCE OF ORDER 𝜶 OF GENERALIZED

DIFFERENCE SEQUENCES

Necip ŞİMŞEK1, Mikail ET2, Vatan KARAKAYA3

1Department of Mathematics, Graduate School of Applied and Natural Sciences, Istanbul Commerce

University, Küçükyalı Campus, Maltepe, Istanbul, Turkey,

[email protected]

2Department of Mathematics, Fırat University, Elazığ, Turkey,

[email protected]

3Department of Mathematical Engineering, Yıldız Technical University, Davutpaşa Campus, Esenler, Istanbul,

Turkey,

[email protected]

Abstract: In this study we introduce the concepts 𝜆𝜈-statistical convergence and strong 𝜆𝜈-

summability of order of generalized difference sequences. Also some relations between 𝑆𝜆𝛼(𝛥𝜈

𝑚)-

statistical convergence and strong 𝑤𝜆𝛽(𝛥𝜈

𝑚 , 𝑝)-summability are given.

Keywords: Cesaro summability, difference sequence, Modulus function, statistical convergence.

References:

[1] Fast, H., “Sur la convergence statistique”, Colloq. Math., 1951, 2, 241-244.

[2] Schoenberg, I. J. “The integrability of certain functions and related summability methods”, Amer.

Math. Monthly, 1959, 66, 361-375.

[3] Connor, J. S. “The Statistical and strong p-Cesaro convergence of sequences”, Analysis, 1988,

8, 47-63.

[4] Edely, O. H. H. ; Mohiuddine, S. A. and Noman, A. K. “Korovkin type approximation theorems

obtained through generalized statistical convergence”, Appl. Math. Let., 2010, 23(11), 1382-1387.

[5] Et, M. ; Cinar, M. and Karakas, M. “On -statistical convergence of order of sequences of

function”, J. Inequal. Appl. 2013, 204, 8 pp.

[6] Fridy, J. “On statistical convergence”, Analysis, 1985, 5, 301-313.



76

ON THE DEFORMATION OF SOME BANACH SEQUENCE SPACES

Necip ŞİMŞEK3, Ruken ÇELİK1, Zhamile ASKEROVA2,

1Department of Mathematics, Graduate School of Applied and Natural Sciences, Istanbul Commerce University,

Küçükyalı Campus, Maltepe, Istanbul, Turkey,

[email protected]

[email protected]

[email protected]

Abstract: In this paper using some moduli of convexity, moduli of smoothness and geometric

properties, we investigate the deformation of some Banach sequence spaces. We will calculate the

certain moduli of some certain sequence spaces and determine the modulus of deformation of the

sequence spaces.

Keywords: uniformly convex, uniformly smooth, modulus of convexity, modulus of smoothness.

References:

[1] J. Banas, K. Fraczek, Deformation Banach Spaces, Comment. Math. Univ. Carolin. 34(1)

(1993), 47--53.

[2] J. Banas, On moduli of Smoothness of Banach Spaces, Bull. Pol. Acad. Sci. Math. 34 (1986),

287--293.

[3] J. A., Clarkson, Uniformly Convex Spaces, Trans. Amer. Math. Soc. 40 (1936), 396--414.

[4] J. Alonso, A. Ullan, Moduli of Convexity, Functional Analysis and Approximation, edited by P.L.

Papini, Bagni di Lucca, Italy, May 16-20, (1988), 25--33.




77

ON KRAWTCHOUK POLYNOMIALS

Nejla ÖZMEN

Department of Mathematics, Düzce University, Düzce, Turkey,

[email protected]

Abstract: In this study deals with some new properties for the Krawtchouk polynomials. The results

obtained here include various families of multilinear and multilateral generating functions,

miscellaneous properties and also some special cases for these polynomials.

Keywords: generating function, summation formula, bilinear and bilateral generating function,

recurrence relations.

References:

[1] H. M. Srivastava and H.L. Manocha, A Treatise on Generating Functions, Halsted Press (Ellis

Horwood Limited, Chichester), John Wiley and Sons, New York, 1984.

[2] N. Özmen and E. Erkus-Duman, Some families of generating functions for the generalized

Ces´aro polynomials, J. Comput. Anal. Appl., 25(4), 670-683 (2018).

[3] N. Özmen and E. Erkus-Duman, Some results for a family of multivariable polynomials, AIP

Conference Proceedings, 1558, 1124 (2013).

[4] P. Feinsilver and J. Kocik, Krawtchouk polynomials and Krawtchouk matrices, Recent

Advances in Applied Probability, 115-141(2005).



78

ASYMPTOTICALLY LACUNARY I-INVARIANT EQUIVALENCE OF

SEQUENCES DEFINED BY A MODULUS FUNCTION

Nimet P. AKIN, Erdinç DÜNDAR and Uğur ULUSU

Department of Mathematics and Science Education, Afyon Kocatepe University, 03200, Afyonkarahisar,

Turkey


[email protected]

[email protected]

[email protected]

Abstract: In this paper, we introduce the concepts of strongly asymptotically lacunary ideal invariant

equivalence, f-asymptotically lacunary ideal invariant equivalence, strongly f-asymptotically lacunary

ideal invariant equivalence and asymptotically lacunary ideal invariant statistical equivalence for

sequences. Also, we investigate some relationships among them.

Keywords: Asymptotically equivalence, Lacunary invariant equivalence, I-equivalence, Modulus

function.

References:

[1] V. Kumar, A. Sharma, Asymptotically lacunary equivalent sequences defined by ideals and

modulus function, Mathematical Sciences, 6(23)2012, 5-pages..


669-686.


762.

[4] H. Nakano, Concave Modulars, J. Math. Soc.Japan, 5(1953), 29-49.


(1963), 81-94.




79

ASYMPTOTICALLY I-INVARIANT EQUIVALENCE OF SEQUENCES DEFINED

BY A MODULUS FUNCTION

Nimet P. AKIN, Erdinç DÜNDAR

Department of Mathematics and Science Education, Afyon Kocatepe University, 03200, Afyonkarahisar,

Turkey


[email protected]

[email protected]

Abstract: In this paper, we introduce the concepts of strongly asymptotically ideal invariant

equivalence, f-asymptotically ideal invariant equivalence, strongly f-asymptotically ideal invariant

equivalence and asymptotically ideal invariant statistical equivalence for sequences. Also, we

investigate some relationships among them.

Keywords: Asymptotically equivalence, Lacunary Invariant equivalence, I-equivalence, modulus

function.

References:

[1] V. Kumar, A. Sharma, Asymptotically lacunary equivalent sequences defined by ideals and

modulus function, Mathematical Sciences, 6(23)2012, 5-pages.


669-686.


762.

[4] H. Nakano, Concave Modulars, J. Math. Soc.Japan, 5(1953), 29-49.


(1963), 81-94.



80

ON FINITE DIMENSIONAL LEIBNIZ ALGEBRAS

Nil MANSUROĞLU1, Mücahit ÖZKAYA2


[email protected]

[email protected]

Abstract: In literature, firstly Leibniz algebras which are generalization of Lie algebras were

introduced as D-algebras by A.M. Bloh. Then, in 1993 these algebras which are called Leibniz

algebras were rediscovered by J.L. Loday. There are many researches on finite dimensional Leibniz

algebras. In this note, our main aim is to focus on finite dimensional Leibniz algebras and to give

some properties for the structure constants of Leibniz algebras.

Keywords: Lie algebra, Leibniz algebra, dimension, structure constant.

Acknowledgement: This work was supported by Kırşehir Ahi Evran University Scientific Research

Projects Coordination Unit. Project Number: FEF.A4.18.009.

References:

[1] Bloh, A.M. A generalization of the concept of Lie algebras, Dokl. Nauk. SSR, 165, 471-473

(1965)

[2] Demir, İ.; Kailash, C.M.; Stitzinger, E. On some structures of Leibniz algebras,

arXiv:1307.7672v1.

[3] Jacobson, N. Lie algebras, Dover, (1979)

[4] Loday, J.L. Une version non commutative des algebres de Lie: les algebres de Leibniz,

L'Enseignement Mathématique, 39, 269-293, (1993)




81

A NEW COMPLEX GENERALIZED BERNSTEIN-SCHURER OPERATOR

Nursel CETIN

Research Department, Turkish State Meteorological Service, Yenimahalle, 06560 Ankara, Turkey,

[email protected]

Abstract: In this paper, we consider the complex form of a new generalization of Bernstein-Schurer

operators and study some approximation properties. We obtain some quantitative estimates and the

exact order of approximation for these operators attached to analytic functions. Also, we prove that

these operators preserve some properties of the original function.

Keywords: complex Stancu operator, complex Bernstein-Schurer operator, quantitative estimates,

simultaneous approximation, exact order of approximation.

References:

[1] Stancu D.D., Quadrature formulas constructed by using certain linear positive operators,

Numerical Integration (Proc. Conf., Oberwolfach, 1981), ISNM 57 (1982) 241-251, Birkhäuser

Verlag, Basel.

[2] Gal S.G., Approximation by Complex Bernstein and Convolution Type Operators, Series on

Concrete and Applicable Mathematics, vol. 8, World Scientific Publishing Co., Pte. Ltd., Hackensack,

NJ, 2009.



82

LACUNARY 𝑰𝟐-INVARIANT CONVERGENCE OF DOUBLE SEQUENCES OF

FUNCTIONS ON AMENABLE SEMIGROUP

Ömer KİŞİ1, Erhan GÜLER2


[email protected]

[email protected]

Abstract: In this study, the concept of lacunary invariant uniform density of any subset A of the set

N×N of double sequences of functions defined on discrete countable amenable semigroups is

defined. Associate with this, the concept of lacunary 𝐼2-invariant convergence for double sequences

of functions defined on discrete countable amenable semigroups is given. Also, we examine

relationships between this new type convergence concept and the concepts of lacunary invariant

convergence and p-strongly lacunary invariant convergence of double sequences of functions on

discrete countable amenable semigroups. Finally, introducing lacunary -invariant convergence

concept and lacunary 𝐼2∗-invariant Cauchy concepts of double sequences of functions on discrete

countable amenable semigroups, we give the relationships among these concepts and relationships

with lacunary 𝐼2-invariant convergence concept.

Keywords: lacunary, Ideal, I-Convergence, Double Sequences of Functions, double sequence,

invariant.

References:

[1] E. Dündar, U. Ulusu and F. Nuray, On ideal invariant convergence of double sequences and

some properties, Creat. Math. Inf., 27(2) (2018).

[2] E. Dündar and B. Altay, 𝐼2-convergence and 𝐼2-Cauchy of double sequences, Acta Math. Sci.,

34B(2) (2014), 343-353.

[3] P.Das, P.Kostyrko, W.Wilczynski, P.Malik, I and 𝐼∗-convergence of double sequences, Math.

Slovaca, 58(5) (2008) 605-620.

[4] U. Ulusu, E. Dündar, F. Nuray, Lacunary 𝐼2-Invariant Convergence and some properties,

International Journal of Analysis and Applications Volume 16, Number 3 (2018), 317-327.

[5] M. Day, Amenable semigroups, Illinois J. Math. 1 (1957) 509–544.

[6] S.A. Douglass, On a concept of summability in amenable semigroups, Math. Scand. 28 (1968)

96-102.

[7] Nuray F., Rhoades B.E., Some kinds of convergence defined by Folner sequences, Analysis

31(4) (2011) 381–390.

[8] Nuray F., Rhoades B.E., Asymptotically and Statistically Equivalent Functions Defined on

Amenable Semigroups, Thai Journal of Mathematics, Volume 11(2) (2013) 303–311.

[9] I. Nomika, Folner’s conditions for amenable semigroups, Math. Scand. 15 (1964) 18–28.




83

A GENERALIZED STATISTICAL CONVERGENCE VIA IDEALS DEFINED BY

FOLNER SEQUENCE ON AMENABLE SEMIGROUPS

Ömer KİŞİ1, Erhan GÜLER2


[email protected]

[email protected]

Abstract: The purpose of this study is to extend the notions of I-convergence, I-limit superior and I-

limit inferior, I-cluster point and I-limit point to functions defined on discrete countable amenable

semigroups. Also, in this paper, we make a new approach to the notions of [V,λ]-summability and λ-

statistical convergence by using ideals and introduce new notions, namely, I-[V,λ]-summability and

I,λ-statistical convergence to functions defined on discrete countable amenable semigroups.

Keywords: inferior, superior, I-Convergence, folner sequence, amenable semigroup.

References:

[1] P. P. Kostyrko, T. Salát, W. Wilezyński, I-Convergence, Real Analysis Exchange Vol. 26(2), pp.

669-686 (2000/2001).

[2] K. Demirci, I-limit superior and limit inferior, Math. Commun. 6 (2001), no. 2, 165--172.

[3] M. Day, Amenable semigroups, Illinois J. Math.1 (1957) 509–544.

[4] S.A. Douglass, On a concept of summability in amenable semigroups, Math. Scand. 28 (1968)

96-102.

[5] Nuray F., Rhoades B.E., Some kinds of convergence defined by Folner sequences, Analysis

31(4) (2011) 381–390.

[6] Nuray F., Rhoades B.E., Asymptotically and Statistically Equivalent Functions Defined on

Amenable Semigroups, Thai Journal of Mathematics, Volume 11(2) (2013) 303–311.

[7] I. Nomika, Folner’s conditions for amenable semigroups, Math. Scand. 15 (1964) 18–28.




84

ON THE NEW SOLUTIONS OF (3+1)-DIMENSIONAL POTENTIAL-YTSF

EQUATION BY 𝒕𝒂𝒏(𝑭(𝝃) 𝟐⁄ )-EXPANSION METHOD

Ozlem KIRCI1, Hasan BULUT2

1Department of Mathematics, Kirklareli University, Kayali Campus, 39000, Kirklareli, Turkey,

[email protected]

2 Department of Mathematics, Firat University, 23200, Elazig, Turkey,

[email protected]

Abstract: In this paper, we employ the 𝑡𝑎𝑛(𝐹(𝜉) 2⁄ )-expansion method to explore the solution

structure of the (3+1)-dimensional potential-YTSF equation. We obtain new solitary wave solutions

in the form of trigonometric function, hyperbolic function, exponential function and rational function.

We also plot two- and three-dimensional graphics of some obtained solutions. In this study, all

computations are performed with the aid of Mathematica 9 and consequently a comprehensive

conclusion is submitted.

Keywords: The 𝒕𝒂𝒏(𝑭(𝝃) 𝟐⁄ )-expansion method, the (3+1)-dimensional potential-YTSF equation,

trigonometric function solutions, hyperbolic function solutions, exponential function solutions, rational

function solutions.

References:

[1] Bulut, H, Sulaiman, T.A., Baskonus H.M.: New Solitary and Optical Wave Structures to the

Korteweg-de Vries Equation with Dual-Power Law Nonlinearity. Opt. Quant. Electron 48 (564), 1-14

(2016)

[2] Kadkhoda N: Exact Solutions of (3+1)-Dimensional Nonlinear Evolution Equations. Caspian

Journal of Mathematical Sciences 4 (2), 189-195 (2015)

[3] Manafian, J: Optical Soliton Solutions for Schrodinger Type Nonlinear Evolution Equations

the 𝑡𝑎𝑛(𝐹(𝜉) 2⁄ )-Expansion Method. Optik- International Journal of Light and Electron Optics 127

(10), 4222-4245 (2016)

[4] Wang, Y-P: Solving the (3+1)-Dimensional Potential-YTSF Equation with Exp-function Method.

Journal of Physics 96, 012186 (2008)




85

CONVERGENCE OF THE INVERSE CONTINUOUS WAVELET TRANSFORM IN

WEIGHTED VARIABLE EXPONENT AMALGAM SPACES

Öznur KULAK1, İsmail AYDIN2

1Department of Banking and Finance, Giresun University, Görele, Giresun, Turkey,

[email protected]

2 Department of Mathematics, Sinop University, Sinop, Turkey,

iaydı[email protected]

Abstract: In this study, we present the some basic properties of the weighted variable exponent

amalgam spaces and investigate the θ-means of f converge to f almost everywhere and in norm for

all f in these spaces under which conditions. Later using these results, we consider norm and almost

everywhere convergence of the inverse continuous wavelet transform in these spaces.

Keywords: weighted variable exponent amalgam spaces, inverse continuous wavelet transform, θ-

summability.

References:

[1] Szarvas, K., Weisz, F. (2014). Continuous Wavelet Transform in Variable Lebesgue Spaces,

Stud. Univ. Babeş-Bolyai Math., 59(4), 497-512.

[2] Weisz, F., (2015). Convergence of the Continuous Wavelet Transform in Winer Amalgam Spaces, De Gruyter, 35(1), 33-46.

[3] Aydın, İ., Gürkanlı, A. T., (2012). Weighted Variable Exponent Amalgam Spaces W(L^p(x)

,L_m^q), Glasnik Matematicki, 47867), 165-174.

[4] Szarvas, K., (2016). Variable Lebesgue Spaces and Continuous Wavelet Transforms, Acta

Mathematica Academiae Paedagogicae Nyiregyhaziensis, 32, 313-325.

[5] Cruz-Uribe, D. V., Fiorenza, A., (2013). Variable Lebesgue Spaces, Foundations and Harmonic

Analysis, New York, NY: Birkhauser/Springer.


mailto:iaydı[email protected]


86

A NEW OPERATOR IDEAL ON BLOCK SEQUENCE SPACES

Pınar ZENGİN ALP1, Emrah Evren KARA2

1,2Department of Mathematics, Düzce University, Konuralp Campus Düzce, Turkey,

[email protected]

[email protected]

Abstract: In this study, we define a new operator ideal on block sequence spaces. Also we give a

quasi-norm on this ideal and show that this class is a quasi-Banach operator ideal.

Keywords: quasi-norm, operator ideal, block sequence space.

References:

[1] D. Foroutannia, On the block sequence space lp (E) and related matrix transformations, Turk J.

Math., (39), 830-841 (2015)

[2] A. Maji, P.D. Srivastava, Some class of operator ideals, Int. J. Pure Appl. Math., 83 (5),731-740

(2013)

[3] A. Pietsch, Operator Ideals, VEB Deutscher Verlag der Wissenschaften, Berlin (1978).




87

ON BICOMPLEX JACOBSTHAL-LUCAS NUMBERS

Serpil HALICI1*, Sevim ASLAN2

1Department of Mathematics, Pamukkale University, Denizli, Turkey

[email protected]

[email protected]

Abstract: In this study, we defined a sequence of bicomplex numbers with coefficients from the

Jacobsthal-Lucas sequence. We investigated some fundamental properties of this new sequence.

Moreover, thanks to the recursive relation that these numbers are, we gave many important

identities.

Keywords: Recurrences; Jacobsthal numbers; bicomplex numbers

Mathematics Subject Classification(2010): 11B37, 11B39, 11B83.

References:

[1] Aydın, T. Bicomplex Fibonacci quaternions. Chaos, Solitons & Fractals, 106(2018),147-153.

[2] Bagchi, B., & A. Banerjee, Bicomplex hamiltonian systems in quantum mechanics. Journal of

Physics A: Mathematical and Theoretical 48(50)(2015) (503001-505402).

[3] Cerin, Z. Sums of Squares and Products of Jacobsthal Numbers, Journal of Integer Sequence

10(2007) Article 07.2.5.

[4] Cockle J, On Systems of Algebra Involving more than one Imaginary, Philosophical Magazine

(series 3) 35 (1849) 434-435.

[5] Djordjevic G. B., Derivative Sequence of Generalized Jacobsthal and Jacobsthal-Lucas

Polynomials, The Fibonacci Quarterly 38(2000) 334-338.

[6] Djordjevic G. B., Generalized Jacobsthal Polynomials, The Fibonacci Quarterly 38(2009) 239-

243.

[7] Flaut, C., & Savin D. Quaternion algebras and generalized Fibonacci Lucas quaternions.

Advances in Applied Clifford Algebras 25(4) (2015) 853-862.

[8] Halici, S. , On Fibonacci quaternions, Adv. in App. Clifford Alg. 22(2) (2012), 321-327.

[9] Halici, S. On complex Fibonacci quaternions. Advances in applied Clifford algebras, 23(1) (2013),

105-112.

[10] Hamilton, W. R. LXXVIII. On quaternions; or on a new system of imaginaries in Algebra: To the

editors of the Philosophical Magazine and Journal. Philosophical Magazine Series 3, 25(169) (1844)

489-495.

[11] Horadam, A. F. Complex Fibonacci numbers and Fibonacci quaternions. The American

Mathematical Monthly, 70(3) (1963), 289-291.




88

ALGEBRA OF CONVERGENCE SET SEQUENCE

Sibel ÖZTÜRK1 and Harun POLAT2

1,2Muş Alparslan University Art and Science Faculty, Department of Mathematics, 49100 Muş,Turkey.


Abstract: There are different convergence notions for sequence of sets, which have significance for

certain applications. Kuratowski convergence, Hausdorff convergence, Wijsman convergence,

Fisher convergence and Mosco convergence are the best known types of convergence. In this study,

we examine algebra of these types of convergent set sequences. Also we characterize the

connections between of their.

Keywords: Kuratowski, Hausdorff, Wijsman, Fisher and Mosco convergence, algebra.

References:

[1] C. Kuratowski, Topology, Academic Press, New York, 1966.

[2] F. Hausdorff , Grundzuge derMengenlehre, Verlag von Veit, Leipzig, Reprinted by Chelsea, New

York1914.

[3] R. A. Wijsman,” Convergence of sequences of convex sets, cones and functions”, Bull. Amer.

Math. Soc. 70 (1964) 186-188.

[4] B. Fisher, “Common fixed points of mappings and set-valued mappings”, Rostock Math. Kolloq.

18 (1981) 69-77.

[5] U. Mosco, “Convergence of convex sets and of solutions of variational inequalities”, Adv. in Math.

3 (1969), 510-585.

[6] M. Baronti, P. Papini, (1986) Convergence of sequences of sets, Methods of functional analysis

in approximation theory, ISNM 76,Birkhauser, Basel.



89

RESULTS ON A CLASS OF HARMONIC UNIVALENT FUNCTIONS INVOLVING

A NEW DIFFERENTIAL OPERATOR

Sibel YALÇIN TOKGÖZ1, Şahsene ALTINKAYA2

1,2Department of Mathematics, Bursa Uludag University, Faculty of Arts and Sciences, 16059 Bursa, Turkey,

[email protected]

[email protected]

Abstract: In this paper, a new subclass of complex-valued harmonic univalent functions involving a

new differential operator is introduced. We investigate necessary and sufficient coefficient bounds,

distortion inequalities, extreme points and inclusion results for this class.

Keywords: harmonic functions, univalent functions, starlike and convex functions, differential

operator.

References:

[1] Altınkaya, Ş and Yalçın, S: On a class of Harmonic univalent functions defined by using a new

differential operator. Theory Appl. Math. Comput. Sci. 6.2 (2016) 125-133.

[2] Bucur, R., L. Andrei and D. Daniel: Coefficient bounds and Fekete-Szegö problem for a class of

analytic functions defined by using a new differential operator. Appl. Math. Sci. 9, 1355–1368. (2015)

[3] Clunie, J, Sheil-Small, T: Harmonic univalent functions. Ann. Acad. Sci. Fenn. Ser. AI Math. 9

(1984) 3-25.

[4] Duren, P.: Harmonic Mappings in the Plane. CRC Press: Cambridge Tracts in Mathematics,

Cambridge University Press (2004).

[5] Jahangiri, J M, Murugusundaramoorthy G and Vijaya, K: Salagean-type harmonic univalent

functions. South J. Pure Appl. Math. 2 (2002) 77-82.




90

CERTAIN CONVEX HARMONIC FUNCTIONS DEFINED BY SUBORDINATION



[email protected]

[email protected]

Abstract: We investigate certain subclass of convex harmonic univalent functions defined by

subordination. We obtain coefficient bounds, distortion theorems, extreme points, convolution and

convex combinations for this class of functions.

Keywords: harmonic functions, univalent functions, convex functions, subordination.

References:

[1] Clunie, J, Sheil-Small, T: Harmonic univalent functions. Ann. Acad. Sci. Fenn. Ser. AI Math. 9,

3-25 (1984)

[2] Dziok, J: Classes of harmonic functions defined by subordination. Abstr. Appl. Anal.

2015.756928 (2015) 1-9.

[3] Kim, Y C, Jahangiri, J M, Choi, J H: Certain convex harmonic functions. Int. J. Math. Math. Sci.

29.8 (2002) 459-465.

[4] Silverman, H: Harmonic univalent functions with negative coefficients. J. Math. Anal. Appl. 220,

283-289 (1998).




91

CERTAIN SUBCLASSES OF HARMONIC UNIVALENT FUNCTIONS

ASSOCIATED WITH A MULTIPLIER LINEAR OPERATOR



[email protected]

[email protected]

Abstract: In the paper, we introduce new subclasses of functions defined by multiplier differential

operator and give coefficient bounds for these subclasses. Also, we obtain necessary and sufficient

convolution conditions, distortion bounds and extreme points for these subclasses of functions.

Keywords: harmonic functions, univalent functions, multiplier transformation, subordination,

modified differential operator.

References:

[1] Altınkaya, Ş and Yalçın, S: On a class of Harmonic univalent functions defined by using a new

differential operator. Theory Appl. Math. Comput. Sci. 6.2 (2016) 125-133.

[2] Clunie, J, Sheil-Small, T: Harmonic univalent functions. Ann. Acad. Sci. Fenn. Ser. AI Math. 9,

3-25 (1984)

[3] Dziok, J: Classes of harmonic functions defined by subordination. Abstr. Appl. Anal.

2015.756928 (2015) 1-9.

[4] Jahangiri, J M, Murugusundaramoorthy G and Vijaya, K: Salagean-type harmonic univalent

functions. South J. Pure Appl. Math. 2, 77-82 (2002).

[5] Yaşar, E and Yalçın, S: Generalized Salagean-type harmonic univalent functions. Stud. Univ.

Babeş-Bolyai Math. 57. 3, 395-403 (2012).




92

An h-DEFORMATION OF SYMPLECTIC (1+2)-SUPERSPACE VIA A

CONTRACTION

Sultan Abaci CELIK1, Canan AYDEMIR2

1,2Department of Mathematics, Yildiz Technical University, Davutpasa Campus, Esenler, 34220 Istanbul,

Turkey,

[email protected]

[email protected]

Abstract: In this study, we introduce an h-deformation of the symplectic superspace 𝑆𝑃1|2 from the

q-deformation via a contraction following the method of [1]. Here we denote q-deformed objects by

primed quantities. Unprimed quantities represent transformed coordinates. We consider the q-

deformed algebra of functions on the quantum symplectic superspace 1|2

qSP generated by 𝜉′, 𝑥′and

𝜂′ with the relations [2]

𝑥′𝜉′ = 𝑞𝜉′𝑥′ , 𝑥′𝜂′ = 𝑞−1𝜂′𝑥′, 𝜂′𝜉′ = −𝑞2𝜉′𝜂′ + 𝑞1/2(1 − 𝑞)𝑥′2 , 𝜉′2 = 0 = 𝜂′2

and we introduce new coordinates , x and with the change of basis in the coordinates of the q-

superspace using the following matrix g [3]:

𝑋′ = (𝜉′

𝑥′

𝜂′

) = (1 0 00 1 0ℎ′ 0 1

) (𝜉𝑥𝜂

) = 𝑔𝑋, ℎ′ =ℎ

2(𝑞 − 1)

Here h is a new deformation parameter that will be replaced by q when 𝑞 → 1.

Keywords: symplectic superspace, q-deformation, h-deformation.

References:

[1] Aghamohammadi, A, Khorrami, M and Shariati, A, h-deformation as a contraction of q-

deformation, J. Phys. A: Math. Gen. 28 (1995): L225-L231.

[2] Aizawa, N, and Chakrabarti, R, Quantum Spheres for (1| 2)qSP , J. Math. Phys. 46

(2005).:103510-1-12.

[3] Celik, S, Covariant differential calculi on quantum symplectic superspace 1|2

qSP , J. Math. Phys.

58 (2017): 023508-1-15.




93

ON A SUBCLASS OF BI-UNIVALENT FUNCTIONS WITH THE FABER

POLYNOMIAL EXPANSIONS

Şahsene ALTINKAYA1, Sibel YALÇIN2

1,2Department of Mathematics, Uludag University, 16059 Bursa, Turkey,

[email protected]

[email protected]

Abstract: In this study, we use the Faber polynomial expansions to obtain upper bounds for

|𝑎𝑛|(𝑛 > 3) coefficients of functions belong to a subclass of bi-univalent functions involving the

Jackson (p,q)-derivative operator in the open unit disc

𝔻 = {𝑧 ∈ ℂ: |𝑧| < 1}.

Keywords: Bi-univalent functions, Faber polynomials, coefficient bounds, quasi-subordination.

References:

[1] Airault, H, and Bouali, H. “Differential calculus on the Faber polynomials.” Bulletin des Sciences

Mathematiques, (2006): 179-222.

[2] Airault, H. “Remarks on Faber polynomials.” Int. Math. Forum 3. (2008): 449-456.

[3] Altınkaya, Ş, and Yalçın, S. “Faber polynomial coefficient estimates for Bi- univalent functions

of complex order based on subordinate conditions involving of the Jackson (p,q)-derivative.”

Miskolc Mathematical Notes 18.(2017): 555-572.

[4] Chakrabarti, R, and Jagannathan, R. “A (p,q)-oscillator realization of two-parameter quantum

algebras.” J. Phys. A: Math. Gen 24. (1991): L711–L718.

[5] P. Duren, Univalent Functions, New York: Grundlehren der Mathematischen Wissenschaften,

Springer, 1983.




94

CHEBYSHEV POLYNOMIAL COEFFICIENT RESULTS ON A SUBCLASS OF

ANALYTIC AND BI-UNIVALENT FUNCTIONS INVOLVING QUASI-

SUBORDINATION



[email protected]

[email protected]

Abstract: In this study, we use the Chebyshev polynomial expansion to construct a new subclass of

bi-univalent functions involving quasi-subordination.

Keywords: Chebyshev polynomials, coefficient bounds, quasi-subordination.

References:

[1] Altınkaya, Ş, and Yalçın, S. “On the Chebyshev polynomial bounds for classes of univalent

functions.” Khayyam Journal of Mathematics 2. (2016): 1-5.

[2] Doha, E. H. “The first and second kind Chebyshev coefficients of the moments of the general-

order derivative of an infinitely differentiable function.” Intern. J. Comput. Math. 51. (1994): 21-35.

[3] Dziok, J, Raina, R. K., and Sokol, J. “Application of Chebyshev polynomials to classes of analytic

functions.” C. R. Acad. Sci. Paris 353. (2015): 433-438.

[4] Z. Nehari, Conformal Mappings, McGraw-Hill, New York, 1952.




95

ON THE BOUNDS OF GENERAL SUBCLASSES OF ANALYTIC AND BI-

UNIVALENT FUNCTIONS ASSOCIATED WITH SUBORDINATION



[email protected]

[email protected]

Abstract: In this study, we define several new subclasses of bi-univalent functions involving a

differential operator in the open unit disc

𝔻 = {𝑧 ∈ ℂ: |𝑧| < 1}.

Moreover, we obtain estimates on the coefficients for functions belonging to these classes.

Keywords: Bi-univalent functions, coefficient bounds, subordination.

References:

[1] Amourah, A, and Darus, M. “Some properties of a new class of univalent functions involving a

new generalized differential operator with negative coefficients.” Indian Journal of Science and

Technology 9. (2016): 1-7.

[2] Brannan, D. A, and Taha, T. S. “On some classes of bi-univalent functions.” Studia Universitatis

Babeş-Bolyai Mathematica 31. (1986): 70-77.

[3] P. Duren, Univalent Functions, New York: Grundlehren der Mathematischen Wissenschaften,

Springer, 1983.

[4] Ch. Pommerenke, Univalent functions, Vandenhoeck and Rupercht, Göttingen, 1975.

[5] Lewin, M. “On a coefficient problem for bi-univalent functions.” Proc. Amer. Math. Soc. 18.

(1967): 63-68.




96

STATISTICAL CONVERGENCE OF MINIMA AND MINIMIZERS OF

SEQUENCES OF FUNCTIONS

Şükrü TORTOP1, Yurdal SEVER1 and ÖZER TALO2

1Department of Mathematics, Afyon Kocatepe University, 03200, Afyonkarahisar, Turkey

2 Yenimahalle, Yunusemre, Manisa, Turkey

[email protected]

[email protected]

[email protected]

Abstract: In this paper, we show that, under some statistical level boundedness assumptions,

statistical epi-convergence of a sequence (fn) to a function f implies the statistical convergence of the

minimum values of (fn) to the minimum value of f. Furthermore, in case (fn) and f have a unique

minimum point, we shall prove that the sequence of the minimizers of (fn) statistically converges to

the minimizer of f.

Keywords: statistical epi-convergence, statistical level boundedness, epigraphs, lower semi

continuity.

References:

[1] Fast, H.: Sur la convergence statistique. Colloq. Math. 2 241-244 (1951)

[2] Fridy, J. A.: Statistical limit points. Proc. Amer. Math. Soc. 118 (4) 1182-1192 (1993)

[3] Fridy, J. A., Orhan, C.: Statistical limit superior and limit inferior. Proc. Amer. Math. Soc. 125

3625-3631 (1997)

[4] Maso, G. D.: An introduction to Γ-convergence, vol.8. Boston (1993)

[5] Wets, R.J-B.: Convergence of convex functions, variational inequalities and convex optimization

problems. New York (1980)





97

ON THE σ-STABLE FAMILIES

Taner BÜYÜKKÖROĞLU1, Özlem ESEN2, Vakıf CAFER3

1,3Department of Mathematics, Eskişehir Technical University, Yunusemre Campus, 26470, Eskişehir, Turkey,

[email protected]

[email protected]

2School for the Handicapped, Anadolu University, Yunusemre Campus,26470, Eskişehir, Turkey,

[email protected]

Abstract: Given a positive number σ, the set of all complex numbers with real parts less than –σ, is

called σ-shifted Hurwitz stability region. For a linear system if all roots of the characteristic polynomial

belong to a shifted region, the system is said to be σ-stable. This property is very important in the

investigation of performance and stability problems. In this report we consider σ-stability problem for

uncertain linear systems. For an interval family, we find the largest value of σ for which the interval

family is stable. We establish sufficient conditions for segment stability which is important for the

application of the Edge theorem.

Keywords: shifted region, interval family, maximal stability region, segment stability.

References:

[1] Bhattacharyya , S.P., Chapellat, H., Keel, L.H., Robust Control: The Parametric Approach, New

Jersey, Prentice-Hall, 1995.

[2] Kawabata, K., Mori, T., Kuroe, Y., Directional Stability Radius: A Stability Analysis Tool for

Uncertain Polynomial Systems, IEEE Transactions on Automatic Control, vol. 48(6), 1012-1016

(2003).

[3] Matsuda, T., Derivation of Robust Stability Ranges for Disconnected Region with Multiple

Parameters, SICE Journal of Control, Measurement, and System Integration, Vol. 10, No. 1, pp. 032–

038 (2017).





98

ON SOME ASYMPTOTICALLY EQUIVALENCE TYPES FOR DOUBLE

SEQUENCES AND RELATIONS AMONG THEM

Uğur ULUSU, Erdinç DÜNDAR


[email protected]

[email protected]

Abstract: In this study, we give definitions of asymptotically lacunary invariant equivalence, strongly

asymptotically lacunary invariant equivalence and asymptotically lacunary ideal invariant

equivalence for double sequences. We also examine the existence of some relations among these

new equivalence definitions.

Keywords: asymptotically equivalence, double sequence, ideal convergence, invariant

convergence, double lacunary sequence.

References:

[1] B. Hazarika, V. Kumar, On asymptotically double lacunary statistical equivalent sequences in

ideal context, Journal of Inequalities and Applications, 2013:543 (2013), 1-15.


669-686.


762.

[4] A. Pringsheim, Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Ann. 53(3) (1900),

289-321.


(1963), 81-94.



99

STATISTICAL LACUNARY INVARIANT SUMMABILITY OF DOUBLE

SEQUENCES

Uğur ULUSU, Esra GÜLLE


[email protected]

[email protected]

Abstract: In this study, we give definitions of lacunary -summability, strongly p-lacunary -

summability and statistical lacunary -summability for double sequences. We also examine the

existence of some relations among the definitions of statistical lacunary -summability, lacunary

invariant statistical convergence and strongly p-lacunary -convergence.

Keywords: statistical convergence, double lacunary sequence, invariant convergence, double

sequence.

References:

[1] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.

[2] S. A. Mohiuddine and E. Savaş, Lacunary statistically convergent double sequences in

probabilistic normed spaces, Ann Univ. Ferrara, 58 (2012), 331-339.

[3] A. Pringsheim, Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Ann. 53(3) (1900),

289-321.


(1963), 81-94.



100

REDUCTION OF NAVIER-STOKES EQUATION TO A LINEAR EQUATION

Waleed KHEDR

Independent Researcher, Cairo, Egypt

[email protected]

Abstract: In this article, we provide two theorems on pointwise coincidence between solutions of

Navier-Stokes equation and solutions of standard linear second order parabolic equations with the

same data. We show that the convection, the pressure, and the external forces (if applied) are

governed by some sort of balance independent of the equation that governs the solution itself. In

light of the well establishment of the theory of existence, regularity and uniqueness of linear second

order parabolic equations, this result represents an important step to fully understand the qualitative

properties of the solutions to Navier-Stokes equation.

Conclusion: In the presence of an 𝐿𝑞 external force 𝑓 = 𝑔 + 𝑘 where 𝑔 = 𝛻𝜙 and𝑘 k are the

components of the Helmholtz-Weyl decomposition, initial profile 𝑣0 ∈ 𝑊1,2(𝛺) and 𝛻 ⋅ 𝑣0 = 0,

and boundary datum 𝑣 ∈ 𝑊1,2(𝜕𝛺) if 𝛺 is bounded ; the following conclusion follows. In arbitrary

domain, Navier-Stokes equation is reduced to a linear parabolic model:

( )

−

−

Ωatv=v

atΩv=v

vatΩvg=p

atΩ=vk,=μΔvv

t

tt

ˆ

0

00

Keywords: Fluid Mechanics, Navier-Stokes equation, Convection

Acknowledgement: This is the abstract of the article submitted to arXiv on 24th of January 2018

with submission number arXiv: submit/2142016.

References:

[1] J. Leray, Etude de diverses equations integrales non lineaires et de quelques problemes que

pose lhydrodynamique, J. Math. Pures Appl., 12, 1933, 1-82.

[2] J. Leray, Essai sur les mouvements plans d'un liquide visqueux que limitent des parois, J.

Math. Pures Appl., 13, 1934, 341-418.

[3] J. Leray, Essai sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Math., 63,

1934, 193-248.

[4] W. S. Khedr, Classical fundamental unique solution for the incompressible Navier-Stokes

equation in RN, Jamp, 5, 939-952, 2017.

[5] W. S. Khedr, Nonconvection and uniqueness in Navier-Stokes equation, arXiv:1706.02552,

2017.



101

EXTENDED KRYLOV METHOD FOR THE NUMERICAL RESOLUTION OF A

LARGE SCALE DIFFERENTIAL SYMMETRIC STEIN EQUATIONS

Yaprak DERICIOGLU1 and Muhammet KURULAY2

1Department of Mathematics, Yildiz Technical University, Istanbul,34220, Turkey

[email protected]

2Department of Mathematical Engineering, Yildiz Technical University, Istanbul, 34220, Turkey

Abstract: In this study, we consider large-scale differential symmetric Stein equations. These matrix

equations have many applications in filtering and image restorations. Our aim is to propose an

iterative method for solution of this problem. The initial problem is projected on a Krylov subspace

then solved by an integration method. We give some numerical examples and theoritical results to

show effectiveness of our method.

Keywords: Large scale systems, Extended Krylov method, Projection methods, Differential

Symmetric Stein equations



102

ON A NEW ESCAPE CRITERIONS FOR COMPLEX POLYNOMIALS USING

FIXED POINT ITERATION METHOD AND S-CONVEXITY

Yunus ATALAN1, Vatan KARAKAYA2

1Department of Mathematics, Aksaray University, Campus, 68100 Aksaray, Turkey,

[email protected]


Istanbul,Turkey,

[email protected]

Abstract: The purpose of this work is to obtain some fixed point results in the generation of fractals

using S*-iteration method with s-convexity for quadratic, cubic and n-th degree polynomials..

Keywords: fractals, fixed point iteration, s-convexity.

References:

[1] Cho, S. Y., Shahid, A. A., Nazeer, W., & Kang, S. M.. “Fixed point results for

fractal generation in Noor orbit and s-convexity”. Springer Plus, 5(1), (2016): 1-16.

[2] Kumari, M. Ashish and R. Chugh, “New Julia And Mandelbrot Sets for a New Faster

Iterative Process”. International Journal of Pure and Applied Mathematics, 107(1), (2016): 161-177.

[3] Partap, N., and Chugh, R.. “Fixed Point Iterative Techniques–An Application to Fractals”. International Journal of Research in Mathematics & Computation. 4(1), (2016): 1-7.




103

A NEW ITERATION METHOD AND SOME FIXED POINT RESULTS

Yunus ATALAN

Department of Mathematics, Aksaray University, 68100, Aksaray, Turkey,

[email protected]

Abstract: In this work, we introduced a new iteration method using almost contraction mappings.

We obtain strong converngence and rate of convergence results for this method. Also we give a data

dependence result for almost contraction mappings by using the new iteration method.

Keywords: new iteration, strong convergence, rate of convergence, data dependence.

References:

[1] Karakaya, V, Atalan,Y, Dogan, K. and Bouzara, NEH.” Some Fixed Point Results For a New

Three Steps Iteration Process in Banach Spaces”.Fixed Point Theory 18(2), 625-640 (2017)

[2] V. Berinde, Iterative Approximation of Fixed Points, Springer, Berlin, 2007.

[3] Phuengrattana, Withun, and Suthep Suantai. "On the Rate of Convergence of Mann, Ishikawa,

Noor and SP Iterations for Continuous on an Arbitrary Interval." J. Comput. Appl. Math. 235(2011),

3006-3914.



104

ON EXISTENCE AND UNIQUINESS OF SOME CLASS NONLINEAR

EIGENVALUE PROBLEM

Yusuf ZEREN1 and Lutfi AKIN2

1Yildiz Technical University, Faculty of Science, Istanbul,Turkey

[email protected]

2Mardin Artuklu University, Faculty of Economics and Business Administration, Mardin, Turkey

[email protected]

Abstract: We will investigate on existence and uniquiness of some class nonlinear eigenvalue

problem.

Keywords: Variable exponent, operator theory, Lebesgue spaces

In this work, we derive a new boundedness and compactness result for the Hardy operator in variable

Lebesgue spaces (VELS) 𝐿𝑝(.)(0, 𝑙). A maximally weak condition is assumed on the exponent

function. For a study the Dirichlet problem of some class nonlinear eigenvalue problem with

nonstandard growth condition the obtained results is applied. In this connection, we mention recent

studies for the multidimensional cases with application of Ambrosetti-Rabinoviche’s Mountain pass

theorem approaches (see, e.g. in [1, 2, 3]) .

Theorem 1. Let 𝑞, 𝑝 ∶ (0, 𝑙) → (1, ∞) be measurable functions with 𝑞(𝑥) ≥ 𝑝(𝑥) on (0, 𝑙) . Assume 𝑝

be monotony increasing and the function 𝑥−

1

𝑝′(𝑥)+𝛿

is almost decreasing on (0, 𝑙).. Then operator H

boundedly acts the space 𝐿𝑝(0, 𝑙) into 𝐿𝑞(.), −

1

𝑝′ −1

𝑞(.)(0, 𝑙). Moreover, the norm of mapping depends

on 𝑝−, 𝑝+, 𝛿, 𝛽.

Theorem 2. Let 𝑞, 𝑝 ∶ (0, 𝑙) → (1, ∞) be measurable functions such that ∞ > 𝑞+ ≥ 𝑞(𝑥) ≥ 𝑝(𝑥) ≥

𝑝− > 1 for all 𝑥 ∈ (0, 𝑙). Assume that 𝑝 be monotony increasing and 𝑥−

1

𝑝′+ is almost decreasing.

Then the identity operator maps boundedly the space 𝑊𝑝(.)1. (0, 𝑙) into 𝐿

𝑞(.),−1

𝑝′ −1

𝑞(.)(0, 𝑙). Moreover,

the norm of mapping is estimated by a constant depending on 𝑝−, 𝑝+, 𝑞, 휀, 𝛽.

Notice, Theorem 2 states the inequality

‖𝑦𝑥 −

1

𝑝′ −1

𝑞(.)‖𝐿𝑞(.)(0,𝑙)

≤ ‖𝑦′‖𝐿𝑝(.)(0,𝑙) (1)

for any absolutely continues function 𝑦: (0, 𝑙) → ℝ with 𝑦(0) = 0.

References:

[1] Ambrosetti, P. Rabinowitz, Dual variational methods in critical point theory and applications, J.

Funct. Anal. 14 , 349–381, 1973.

[2] F.I. Mamedov and A. Harman On a Hardy type general weighted inequality in spaces

𝐿𝑝(.)(0, 𝑙). Integr. Equ. Oper. Th., 66(1), 565-592, 2010.

[3] V. D. Radulescu, Nonlinear elliptic equations with variable exponent: Old and new, Nonlinear

Analysis, 121, 336–369, 2015.




105

OBTAINING THE FINITE DIFFERENCE APPROXIMATION OF TRANSMISSION

CONDITIONS OF DEFORMATION PROBLEM FOR MULTILAYERED

MATERIALS

Zahir MURADOGLU1, Vildan YAZICI1, Tatsiana URBANOVICH1,2

1Department of Mathematics, Kocaeli University, Izmit, Turkey,


2Department of Higher Mathematics, Polotsk State University, Belarus

[email protected]

Abstract: In this study, we use finite element method to obtain the numerical solution of the plane

deformation problem for multilayered materials. The mathematical model of the problem is expressed

by the system of Lame equations. Some differences of the mechanical properties of the materials

composed the layers make it impossible to solve such problems with classical finite difference

methods. In this work, to ensure continuity at the common boundary between the layers, we obtain

the numerical expressions of the transmission conditions by using the finite element method. The

relation between the numerical expressions obtained by using finite element method and finite

differences method is shown.

Keywords: Finite element method, Lame equation, Laminated medium; transmission conditions.

Acknowledgement: This work is supported by the TUBITAK program 2221 - "Fellowship Program

For Visiting Scientists and Scientists on Sabbatical Leave".

References:

[1] G.M.L. Gladwell, Contact Problems in the Classical Theory of Elasticity, Sijthoff and Noordhoff,

Alphen aan den Rijn, The Netherlands, 1980.

[2] N.J. Pindera, M.S. Lane, Frictionless contact of layered half-planes, ASME J. Appl. Mech. 60

(1993) 633–645.

[3] Z. Seyidmamedov, Finite-element analysis of frictionless contact problem for a laminated

medium, Mathematics and Computers in Simulation 58 (2002) 111–123.





106

POSTER SESSION

SUMS OF ELEMENT ORDERS IN FINITE GROUPS

Ayşe Nur KÖKSAL1, Nil MANSUROĞLU2


[email protected]

[email protected]

Abstract: We investigate the sum of element orders of finite groups in literature and, our purpose is

to formulate the sum of element orders of symmetric groups in the light of works and used methods

in articles of H. Amiri, S.M. Jafarian Amiri and I.M. Isaacs with M. Tarnauceanu and D. Gregorian

Fodor.

Keywords: finite group, element order, sum of element orders.

References:

[1] H. Amiri, S.M. Jafarian Amiri, I.M. Isaacs, Sums of element orders in finite groups, Comm.

Algebra, 37, (2009), 2978-2980.

[2] M. Tarnauceanu, D. Gregorian Fodor, On the sum of element orders of finite abelian groups,

10.2478/ aicu-2013-0013.

[3] H. Amiri, S.M. Jafarian Amiri, Sum of element orders on finite groups of the same order, J.

Algebra Appl., 10 (2), (2011), 187-190.




107

APPROXIMATION BY GENERALIZED COMPLEX SZÁSZ-MIRAKYAN

OPERATORS IN COMPACT DISK

Döne KARAHAN1, Sevilay K. SERENBAY2, Aydın İZGİ3

1,2,3Department of Mathematics, Harran University, Osmanbey Campus, Şanlıurfa, Turkey,

[email protected]

[email protected]

[email protected]

Abstract: In this study, the generalized complex Szász-Mirakyan operators are introduced and the

approximation properties of these operators are studied. The Voronovskaya's theorem with

quantitative estimate for these operators attached to analytic function is obtained on compact disks.

Keywords: Complex Szász-Mirakyan operators, quantitative exact approximation, Voronovskaya's

theorem

References:

[1] Lorentz, G.G: Bernstein polynomials, 2nd edn. Chelsea, New York, ISBN:0-8284-0323-6

(1986).

[2] Gal GS. Approximation by complex Bernstein and convolution type operators. World Scienti_c

Publ. Co., Singapore (2009).

[3] Serenbay, S.K, Dalmanoglu, O: Rate of convergence for generalized Szász-Mirakyan operators

in exponential weighted space. Applications and Applied Math. 12:2, 884-897 (2017).

[4] Gupta, V, Verma, K.D: Approximation by complex Favard-Szász-Mirakjan-Stancu operators in

compact disks. Mathematical Sciences. 6:25 (2012).

[5] Korovkin, P. P: On convergence of linear positive operators in the space of continuous

functions. Dokl. Akad. Nauk, 90, 961-964 (1953).

[6] Kantorovich, L. V: Sur certains developments suivant les polynomes de la forms de S.Bernstein

I, II, Dokal Akad Nauk SSSR, 595-600, 563-568, (1930).





108

ON APPROXIMATION BY GENERALIZED BERNSTEIN-KANTOROVICH

OPERATORS OF TWOVARIABLE

Döne KARAHAN1, Aydın İZGİ2

1,2Department of Mathematics, Harran University, Osmanbey Campus, Şanlıurfa, Turkey,

[email protected]

[email protected]

Abstract: In this study, the generalized Bernstein-Kantorovich type operators are introduced and

some approximation properties of these operators are studied in the space of continuous functions

of two variables on a compact set . The convergence rate of these operators are obtained by means

of the modulus of continuity. The Voronovskaya type theorem is given and some differential

properties of these operators are proved.

Keywords: Bernstein-Kantorovich type operator, modulus of continuity, Voronovskaya type

theorem.

References:

[1] Bernstein, S. N: Demonstration du theorem de Weierstrass fondee sur le calculu des

probabilites. Comp. Comm. Soc. Mat. Charkow Ser., 13(2), 1-2 (1912).

[2] Kantorovich, L. V: Sur certains developments suivant les polynomes de la forms de S.Bernstein

I, II, Dokal Akad Nauk SSSR, 595-600, 563-568, (1930).

[3] Korovkin, P. P: On convergence of linear positive operators in the space of continuous

functions. Dokl. Akad. Nauk, 90, 961-964 (1953).




109

NON PRESENTING PARTICIPANTS

Zhamile ASKEROVA Arzu d. OĞUZ Fatih DERİNGÖZ İsmail Onur KIYMAZ Ayşegül ÇETİNKAYA Emirhan HACIOĞLU Cem OĞUZ Sezin AYKURT SEPET Zehra GÜZEL ERGÜL Hasan ALTINBAŞ Şebnem YILDIZ Hatice ÖZKAN Sena HALICI Fatma ÇOLAK Hasan BULUT Emine ÖNAL KIR Emre TAŞ Faruk YILMAZ Farah M. MİSLAR Yasin KARAKAYA Tuba DEMİRAY Reyhan ÖZÇELİK Nil MANSUROĞLU Nagehan KILINÇ GEÇER Cenk YILDIRIM Musa DİKMEN M.Fatih KARAASLAN Gülden GÜRSOY Fatma KOÇAKER ALTUN Yılmaz ALTUN Zhor MELLAH A. Canan GÜNEŞ Merve DEMİREL Esra Nur SOYLU Guyguy Mande MABEKE Oulgiht BADR Dada LASSYED Adeeb SAEED Abduraxim ABDUGANIYEV Isaac Kwabena ADOMAKO Jonathan Osei OWUSU Abdullah ANSARI Gülistan İSKANDAROVA Kader ŞİMŞİR ACAR Caner KAZAR

İstanbul Commerce University Atılım University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Yildiz Technical University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Düzce University Fırat University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Düzce University Düzce University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Yildiz Technical University Adıyaman University Yildiz Technical University Şehit Cem Özgül OO. Kırşehir Ahi Evran University Kırşehir Ahi Evran University University Mohammed First, Oujda Kırşehir Ahi Evran University Kırşehir Ahi Evran University Ege University Mathematic and Computer Shardfo-tech Company Limited Shardfo-tech Company Limited Amu İstanbul Commerce University Yildiz Technical University Yildiz Technical University


110

INDEX

A

Aakif Fairooze TALEE .................................................. 73

Abdulmajid NUSAYR ................................................... 18

Akhilesh PRASAD ........................................................ 19

Arife Aysun KARAASLAN ......................................... 7, 20

Arzu ÖZKOÇ ÖZTÜRK .................................................. 21

Asıf YOKUS ................................................................. 22

Aydın İZGİ.................................................... 74, 108, 107

Aynur ŞAHİN .............................................................. 23

Ayşe Nur KÖKSAL ...................................................... 106

Ayşe SARIAYDIN-FİLİBELİOĞLU .................................... 24

B

Bayram ŞAHİN .............................................................. 6

Burak KURT ................................................................ 25

C

Canan AYDEMIR ......................................................... 92

Cihan UNAL ..................................................... 26, 57, 58

Cuneyt YAZICI ............................................................. 27

D

Derya KARATAŞ .......................................................... 28

Derya SEKMAN ......................................................29, 30

Dogan KAYA ............................................................... 31

Döne KARAHAN ................................................. 107, 108

Driss KARIM ............................................................... 55

Duran TURKOGLU ....................................................... 49

E

Emrah Evren KARA ................................................32, 86

Erdal ÜNLÜYOL ........................................................... 33

Erdinç DÜNDAR .................................... 34, 78, 79, 98, 63

Erhan GÜLER ............................................. 35, 36, 82, 83

Erkut ALİMERT.......................................................... 103

Esra GÜLLE ............................................................37, 99

F

Faik GÜRSOY ............................................ 6, 7, 38, 69, 72

Fatih NURAY ........................................................... 6, 34

Ferhat SAH ............................................................39, 40

Fernane KHAIREDDINE ................................................ 41

Fuat USTA .................................................................. 42

Funda TAŞDEMİR ........................................................ 43

G

G. Canan HAZAR GÜLEÇ .............................................. 44

G. Zamani ESKANDANI ................................................ 45

Gonca DURMAZ .......................................................... 46

Gulistan ISKANDAROVA .............................................. 31

H

Haci Mehmet BASKONUS ...................................... 47, 48

Hakan SAHIN .............................................................. 49

Hamdullah ŞEVLİ..................................................... 6, 50

Hamid VAEZI .............................................................. 51

Handan KOSE ............................................................. 52

Harun POLAT ........................................................ 54, 88

Hasan BULUT .............................................................. 84

Hassan MOUADI ......................................................... 55

Hatice ASLAN HANÇER ................................................ 46

Havva TİLKİ ................................................................. 53

Hulya KODAL SEVİNDİR ............................................... 27

I

Ismail AYDIN .................................................... 26, 57, 58

İ

İbrahim GÖKCAN ........................................................ 56

İshak ALTUN ......................................................... 46, 49

İsmail AYDIN ............................................................... 85

İsmail TAŞTEKİN .......................................................... 43

J

Javid ALI ....................................................................... 7

Jong Kyu KIM .............................................................. 14

K

Kadri DOĞAN ........................................................ 59, 60

L

Lutfi AKIN ................................................................. 104


111

M

M. Ali SARIGÖ2 ........................................................... 44

M. RAEISI ................................................................... 45

M. SARI ...................................................................... 68

M. Yahya ABBASI ........................................................ 73

Mehmet GÜRDAL ....................................................... 53

Merve İLKHAN ............................................................ 61

Mikail ET .................................................................... 75

Mohamad NAGHLISAR ................................................ 51

Mohammad KNEFATI .................................................. 62

Mohammad MURSALEEN ................................ 5, 6, 7, 15

Mualla Birgül HUBAN .................................................. 53

Muhammed Recai TÜRKMEN ..................... 63, 64, 65, 66

Muhammet KURULAY ............................................... 101

Murat KİRİŞCİ ............................................................. 67

Murat OLGUN ............................................................ 46

Musa DİKMEN ............................................................ 69

Muttalip ÖZAVŞAR...................................................... 70

Mücahit ÖZKAYA ........................................................ 71

Müzeyyen ERTÜRK ................................................72, 38

N

Nadire Fulda ODABAŞI ................................................ 74

Necip ŞİMŞEK ........................................................75, 76

Nejla ÖZMEN .............................................................. 77

Nil MANSUROĞLU ......................................... 28, 71, 106

Nimet P. AKIN........................................................78, 79

Nursel CETIN .............................................................. 81

O

Ozlem KIRCI ................................................................ 84

Ö

Ömer KİŞİ .................................................. 82, 83, 35, 36

ÖZER TALO ................................................................. 96

Özlem ESEN ................................................................ 97

Öznur KULAK .............................................................. 85

P

Pınar ZENGİN ALP ....................................................... 86

Q

Qamrul Hasan ANSARI ............................................ 5, 13

R

Ruken ÇELİK ............................................................... 76

S

S. Ali-TAHIR ................................................................ 68

Sabahat Ali KHAN ....................................................... 73

Serpil HALICI ............................................................... 87

Sevilay K. SERENBAY ................................................. 107

Sevim ASLAN .............................................................. 87

Sibel ÖZTÜRK.............................................................. 88

Sibel YALÇIN TOKGÖZ ..................... 89, 90, 91, 93, 94, 95

Suleyman CETINKAYA ................................................. 27

Sultan Abaci CELIK ...................................................... 92

Ş

Şahsene ALTINKAYA........................ 93, 94, 95, 89, 90, 91

Şükrü TORTOP ............................................................ 96

T

Taner BÜYÜKKÖROĞLU ............................................... 97

Tanuj KUMAR ............................................................. 19

Tatsiana URBANOVICH.............................................. 105

U

Uğur ULUSU ......................................... 34, 37, 78, 98, 99

V

Vakıf CAFER ................................................................ 97

Vatan KARAKAYA ........................ 4, 7, 20, 29, 30, 62, 102

Vildan YAZICI ............................................................ 105

W

Waleed KHEDR ......................................................... 100

Y

Yaprak DERICIOGLU .................................................. 101

Yeter ERDAŞ ............................................................... 33

Yılmaz ALTUN ............................................................. 59

Yunus ATALAN ................................................... 102, 103

Yurdal SEVER .............................................................. 96

Yusuf ZEREN ............................................................. 104

Z

Zahir MURADOGLU ................................................... 105

Zhamile ASKEROVA ..................................................... 76

Zuhair NASHED ....................................................... 6, 16

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4th - Kırşehir Ahi Evran University€¦ · It was a great moment of excitement when Prof. (Dr.) Vatan Karakaya, Rector, Ahi Evran University, discussed with me the matter of organizing