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Article Citation - Scopus: 1Some Remarks About the Existence of Coupled g-coincidence Points(Springeropen, 2015) Erhan, Inci M.; Roldan-Lopez-de-Hierro, Antonio-Francisco; Shahzad, NaseerVery recently, in a series of subsequent papers, Nan and Charoensawan introduced the notion of g-coincidence point of two mappings in different settings (metric spaces and G-metric spaces) and proved some theorems in order to guarantee the existence and uniqueness of such kind of points. Although their notion seems to be attractive, in this paper, we show how this concept can be reduced to the unidimensional notion of coincidence point, and how their main theorems can be seen as particular cases of existing results. Moreover, we prove that the proofs of their main statements have some gaps.Article Citation - WoS: 1Citation - Scopus: 2Common Fixed Point of Multifunctions on Partial Metric Spaces(Springer international Publishing Ag, 2015) Aleomraninejad, S. Mohammad Ali; Erhan, Inci M.; Kutbi, Marwan A.; Shokouhnia, MasoumehIn this paper, some multifunctions on partial metric space are defined and common fixed points of such multifunctions are discussed. The results presented in the paper generalize some of the existing results in the literature. Several conclusions of the main results are given.Article Citation - WoS: 11Citation - Scopus: 8Coupled Coincidence Point and Coupled Fixed Point Theorems via Generalized Meir-Keeler Type Contractions(Hindawi Ltd, 2012) Aydi, Hassen; Karapinar, Erdal; Erhan, Inci M.We prove coupled coincidence point and coupled fixed point results of F : X x X -> X and g : X -> X involving Meir-Keeler type contractions on the class of partially ordered metric spaces. Our results generalize some recent results in the literature. Also, we give some illustrative examples and application.Article Citation - WoS: 11Citation - Scopus: 20The Taylor Series Method and Trapezoidal Rule on Time Scales(Elsevier Science inc, 2020) Georgiev, Svetlin G.; Erhan, Inci M.The Taylor series method for initial value problems associated with dynamic equations of first order on time scales with delta differentiable graininess function is introduced. The trapezoidal rule for the same types of problems is derived and applied to specific examples. Numerical results are presented and discussed. (c) 2020 Elsevier Inc. All rights reserved.Article ON A GENERALIZED α-ADMISSIBLE RATIONAL TYPE CONTRACTIVE MAPPING(Yokohama Publ, 2016) Erhan, Inci M.; Kir, MehmetRecently, many generalized contractive conditions which involve rational contractive inequalities have been introduced in the context of partially ordered metric spaces. In this paper, we aim to give a generalized rational contractive condition which involves some of these results without need of extra restrictions.Article Citation - WoS: 144Citation - Scopus: 156Uniqueness of Solution for Higher-Order Nonlinear Fractional Differential Equations With Multi-Point and Integral Boundary Conditions(Springer-verlag Italia Srl, 2021) Sevinik-Adiguzel, Rezan; Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.This study is devoted to the development of alternative conditions for existence and uniqueness of nonlinear fractional differential equations of higher-order with integral and multi-point boundary conditions. It uses a novel approach of employing a fixed point theorem based on contractive iterates of the integral operator for the corresponding fixed point problem. We start with developing an existence-uniqueness theorem for self-mappings with contractive iterate in a b-metric-like space. Then, we obtain the unique solvability of the problem under suitable conditions by utilizing an appropriate b-metric-like space.Article Citation - WoS: 32Citation - Scopus: 45Fixed Point Theorems for a Class of Α-Admissible Contractions and Applications To Boundary Value Problem(Hindawi Publishing Corporation, 2014) Alsulami, Hamed H.; Gulyaz, Selma; Karapinar, Erdal; Erhan, Inci M.A class of alpha-admissible contractions defined via altering distance functions is introduced. The existence and uniqueness conditions for fixed points of such maps on complete metric spaces are investigated and related fixed point theorems are presented. The results are reconsidered in the context of partially ordered metric spaces and applied to boundary value problems for differential equations with periodic boundary conditions.Article Citation - WoS: 52Citation - Scopus: 62F-Contraction Mappings on Metric-Like Spaces in Connection With Integral Equations on Time Scales(Springer-verlag Italia Srl, 2020) Agarwal, Ravi P.; Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.In this paper we investigate the existence and uniqueness of fixed points of certain (phi,F)-type contractions in the frame of metric-like spaces. As an application of the theorem we consider the existence and uniqueness of solutions of nonlinear Fredholm integral equations of the second kind on time scales. We also present a particular example which demonstrates our theoretical results.Article Citation - WoS: 1Citation - Scopus: 4Fixed Point Theorems for Mappings With a Contractive Iterate at a Point in Modular Metric Spaces(House Book Science-casa Cartii Stiinta, 2022) Karapinar, Erdal; Aksoy, Umit; Fulga, Andreea; Erhan, Inci M.In this manuscript, we introduce two new types of contraction, namely, w-contraction and strong Sehgal w-contraction, in the framework of modular metric spaces. We indicate that under certain assumptions, such mappings possess a unique fixed point. For the sake of completeness, we consider examples and an application to matrix equations.Article Citation - WoS: 3Citation - Scopus: 6Fixed Points of Α-Admissible Meir-Keeler Contraction Mappings on Quasi-Metric Spaces(Springer international Publishing Ag, 2015) Alsulami, Hamed H.; Gulyaz, Selma; Erhan, Inci M.We introduce alpha-admissible Meir-Keller and generalized alpha-admissible Meir-Keller contractions on quasi-metric spaces and discuss the existence of fixed points of such contractions. We apply our results to G-metric spaces and express some fixed point theorems in G-metric spaces as consequences of the results in quasi-metric spaces.
