Browsing by Author "Karapinar, Erdal"

Now showing 1 - 20 of 308

Citation - WoS: 5
Advances on Fixed Point Results on Partial Metric Spaces
(Springer international Publishing Ag, 2019) Karapinar, Erdal; Tas, Kenan; Rakocevic, Vladimir; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
[No Abstract Available]
Advances on Multivalued Operators and Related Fixed Point Problems
(Hindawi Publishing Corporation, 2014) Chen, Chi-Ming; Karapinar, Erdal; Du, Wei-Shih; Aydi, Hassen; Romaguera, Salvador; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
[No Abstract Available]
Citation - WoS: 23
Citation - Scopus: 26
Alpha-Psi Contractions on Generalized Metric Spaces
(Springer, 2014) Asadi, Mehdi; Karapinar, Erdal; Kumar, Anil; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this work, we introduce the class of alpha-psi-Geraghty contraction as well as generalized alpha-psi-Geraghty contraction mappings in the context of generalized metric spaces where psi is an auxiliary function which does not require the subadditive property and set up some fixed point results for both classes individually. Our results will extend, improve and generalize several existing results in the literature.
Applications of Non-Unique Fixed Point Theorem of Ciric To Nonlinear Integral Equations
(int Center Scientific Research & Studies, 2019) Sevinik-Adiguzel, Rezan; Karapinar, Erdal; Erhan, Inci M.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper we discuss the application of the non-unique fixed point theorem of Ciric to nonlinear Fredholm integral equations. We establish an existence theorem for the solutions of such integral equations and apply the theorem to particular examples.
Citation - WoS: 69
Citation - Scopus: 70
An Approach To Best Proximity Points Results Via Simulation Functions
(Springer Basel Ag, 2017) Karapinar, Erdal; Khojasteh, Farshid; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we investigate of the existence of the best proximity points of certain mapping defined via simulation functions in the frame of complete metric spaces. We consider the uniqueness criteria for such mappings. The obtained results unify a number of the existing results on the topic in the literature.
Citation - WoS: 16
Citation - Scopus: 31
An Approach To Existence of Fixed Points of Generalized Contractive Multivalued Mappings of Integral Type Via Admissible Mapping
(Hindawi Ltd, 2014) Ali, Muhammad Usman; Kamran, Tayyab; Karapinar, Erdal; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
We investigate the existence of a fixed point of certain contractive multivalued mappings of integral type by using the admissible mapping. Our results generalize the several results on the topic in the literature involving Branciari, and Feng and Liu. We also construct some examples to illustrate our results.
Citation - WoS: 8
Citation - Scopus: 8
Berinde Mappings in Ordered Metric Spaces
(Springer-verlag Italia Srl, 2015) Karapinar, Erdal; Sadarangani, Kishin; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Recently, Samet and Vetro proved a fixed point theorem for mappings satisfying a general contractive condition of integral type in orbitally complete metric spaces (Samet and Vetro, Chaos Solitons Fractals 44:1075-1079, 2011). Our aim in this paper is to present a version of the results obtained in the above mentioned paper in the context of ordered metric spaces. Some examples are presented to distinguish our results from the existing ones.
Citation - WoS: 23
Citation - Scopus: 32
Berinde-Type Generalized Contractions on Partial Metric Spaces
(Hindawi Ltd, 2013) Aydi, Hassen; Amor, Sana Hadj; Karapinar, Erdal; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
We consider generalized Berinde-type contractions in the context of partial metric spaces. Such contractions are also known as generalized almost contractions in the literature. In this paper, we extend, generalize, and enrich the results in this direction. Some examples are presented to illustrate our results.
Citation - WoS: 17
Best Approximations Theorem for a Couple in Cone Banach Space
(Springer, 2010) Karapinar, Erdal; Turkoglu, Duran; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
The notion of coupled fixed point is introduced by Bhaskar and Lakshmikantham, (2006). In this manuscript, some result of Mitrovic, (2010) extended to the class of cone Banach spaces.
Citation - WoS: 4
Best Proximity Point for Certain Proximal Contraction Type Mappings
(Univ Prishtines, 2018) Alqahtani, Badr; Hamzehnejadi, Javad; Karapinar, Erdal; Lashkaripour, Rahmatollah; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we introduce the new notion of generalized proximal alpha-h-phi-contraction mappings and investigate the existence of the best proximity point for such mappings in the complete metric spaces.
Citation - WoS: 2
Citation - Scopus: 9
Best Proximity Point for Generalized Proximal Weak Contractions in Complete Metric Space
(Hindawi Ltd, 2014) Karapinar, Erdal; Pragadeeswarar, V.; Marudai, M.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
We introduce a new class of nonself-mappings, generalized proximal weak contraction mappings, and prove the existence and uniqueness of best proximity point for such mappings in the context of complete metric spaces. Moreover, we state an algorithm to determine such an optimal approximate solution designed as a best proximity point. We establish also an example to illustrate our main results. Our result provides an extension of the related results in the literature.
Citation - WoS: 56
Best Proximity Point on Different Type Contractions
(Natural Sciences Publishing Corp-nsp, 2011) Karapinar, Erdal; Erhan, Inci M.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this manuscript, some proximity points are obtained by using different types cyclic contractions. Also, generalized cyclic Meir Keeler contraction is introduced and a new fixed point theorem for this cyclic mapping is stated.
Citation - WoS: 15
Citation - Scopus: 21
A Best Proximity Point Result in Modular Spaces with the Fatou Property
(Hindawi Ltd, 2013) Jleli, Mohamed; Karapinar, Erdal; Samet, Bessem; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Consider a nonself-mapping T: A -> B, where (A, B) is a pair of nonempty subsets of a modular space. X-rho. A best proximity point of T is a point z is an element of A satisfying the condition: rho(z - Tz) = inf {rho(x-y) : (x,y) is an element of A x B}. In this paper, we introduce the class of proximal quasicontraction nonself-mappings in modular spaces with the Fatou property. For such mappings, we provide sufficient conditions assuring the existence and uniqueness of best proximity points.
Citation - WoS: 9
Citation - Scopus: 13
Best Proximity Point Results for Mk-Proximal Contractions
(Hindawi Publishing Corporation, 2012) Jleli, Mohamed; Karapinar, Erdal; Samet, Bessem; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Let A and B be nonempty subsets of a metric space with the distance function d, and T : A -> B is a given non-self-mapping. The purpose of this paper is to solve the nonlinear programming problem that consists in minimizing the real-valued function x bar right arrow. d (x, Tx), where T belongs to a new class of contractive mappings. We provide also an iterative algorithm to find a solution of such optimization problems.
Citation - WoS: 13
Citation - Scopus: 13
Best Proximity Point Results in Dislocated Metric Spaces Via r-functions
(Springer-verlag Italia Srl, 2018) Gholizadeh, Leila; Karapinar, Erdal; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we investigate the existence of best proximity of R-contractions in the frame of dislocated metric spaces. We also propose some conditions to guarantee the uniqueness of best proximity point for such contractions. We consider an illustrative example to support the given results. This result generalizes a number of recent results on the topic in the literature.
Citation - WoS: 19
Citation - Scopus: 18
Best Proximity Point Theorems for kt-types Cyclic Orbital Contraction Mappings
(House Book Science-casa Cartii Stiinta, 2012) Karapinar, Erdal; Petrusel, Gabriela; Tas, Kenan; Mathematics; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this manuscript, three new KT-types cyclic orbital contractions are defined and some related best proximity point theorems are given. Also, the notion of KT-type cyclic orbital Meir-Keeler contraction is defined and some fixed point theorems for this class of mappings are proved. The results of this manuscript generalize some theorems, on the same subject, of several authors, such as Kirk-Srinavasan-Veeramani, Eldered-Veeramani and Karpagam-Agrawal.
Citation - WoS: 24
Citation - Scopus: 29
Best proximity points and extension of Mizoguchi-Takahashi's fixed point theorems
(Springer int Publ Ag, 2013) Kumam, Poom; Aydi, Hassen; Karapinar, Erdal; Sintunavarat, Wutiphol; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we introduce a multi-valued cyclic generalized contraction by extending the Mizoguchi and Takahashi's contraction for non-self mappings. We also establish a best proximity point for such type contraction mappings in the context of metric spaces. Later, we characterize this result to investigate the existence of best proximity point theorems in uniformly convex Banach spaces. We state some illustrative examples to support our main theorems. Our results extend, improve and enrich some celebrated results in the literature, such as Nadler's fixed point theorem, Mizoguchi and Takahashi's fixed point theorem.
Citation - WoS: 58
Best Proximity Points for Generalized α-ψ-Proximal Contractive Type Mappings
(Hindawi Ltd, 2013) Jleli, Mohamed; Karapinar, Erdal; Samet, Bessem; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
We introduce a new class of non-self-contractive mappings. For such mappings, we study the existence and uniqueness of best proximity points. Several applications and interesting consequences of our obtained results are derived.
Citation - WoS: 69
Citation - Scopus: 67
Best Proximity Points of Cyclic Mappings
(Pergamon-elsevier Science Ltd, 2012) Karapinar, Erdal; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this this manuscript, we proved that the existence of best proximity points for the cyclic operators T defined on a union of subsets A, B of a uniformly convex Banach space X with T (A) subset of B, T(B) subset of A and satisfying the condition parallel to Tx - Yy parallel to <= alpha/3[parallel to x-y parallel to + parallel to Tx - x parallel to + parallel to Ty - y parallel to] + (1 - alpha)diam(A, B) for alpha is an element of (0, 1) and for all x is an element of A, for all y is an element of B, where diam(A, B) = inf{parallel to x - y parallel to : x is an element of A, y is an element of B}. (C) 2012 Elsevier Ltd. All rights reserved.
Citation - WoS: 21
Citation - Scopus: 23
Best Proximity Points of Generalized Almost Ψ-Geraghty Contractive Non-Self
(Springer international Publishing Ag, 2014) Aydi, Hassen; Karapinar, Erdal; Erhan, Inci M.; Salimi, Peyman; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we introduce the new notion of almost psi-Geraghty contractive mappings and investigate the existence of a best proximity point for such mappings in complete metric spaces via the weak P-property. We provide an example to validate our best proximity point theorem. The obtained results extend, generalize, and complement some known fixed and best proximity point results from the literature.