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Article Citation - WoS: 51Citation - Scopus: 58F-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 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: 13Fixed Point Theorems for (α, Ψ)-Meir Mappings(int Scientific Research Publications, 2015) Redjel, Najeh; Dehici, Abdelkader; Karapinar, Erdal; Erhan, Inci M.In this paper, we establish fixed point theorems for a (alpha, psi)-Meir-Keeler-Khan self mappings. The main result of our work is an extension of the theorem of Khan [M. S. Khan, Rend. Inst. Math. Univ. Trieste. Vol VIII, Fase., 10 (1976), 1-4]. We also give some consequences. (C)2015 All rights reserved.Article Citation - WoS: 56Best Proximity Point on Different Type Contractions(Natural Sciences Publishing Corp-nsp, 2011) Karapinar, Erdal; Erhan, Inci M.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.Article Citation - WoS: 3Citation - Scopus: 3On the Fixed Points of Iterative Contractive Mappings Defined Via Implicit Relation(Taylor & Francis Ltd, 2021) Aksoy, Umit; Erhan, Inci M.; Fulga, Andreea; Karapinar, ErdalIn this paper, we consider an implicit relation to generalize iterative fixed point results in the literature in the context of metric spaces. We conclude that several existing results are immediate consequences of our main results.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 Citation - WoS: 141Citation - Scopus: 144Uniqueness 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: 25Citation - Scopus: 32Fixed Point Theorems in Complete Modular Metric Spaces and an Application To Anti-Periodic Boundary Value Problems(Univ Nis, Fac Sci Math, 2017) Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.In this paper existence and uniqueness of fixed points for a general class of contractive and nonexpansive mappings on modular metric spaces is discussed. As an application of the theoretical results, the existence of a solution of anti-periodic boundary value problems for nonlinear first order differential equations of Caratheodory's type is considered in the framework of modular metric spaces.Article Citation - WoS: 167Citation - Scopus: 168Fixed Point Theorems for Operators on Partial Metric Spaces(Pergamon-elsevier Science Ltd, 2011) Karapinar, Erdal; Erhan, Inci M.Fixed point theorems for operators of a certain type on partial metric spaces are given. Orbitally continuous operators on partial metric spaces and orbitally complete partial metric spaces are defined, and fixed point theorems for these operators are given. (C) 2011 Elsevier Ltd. All rights reserved.
