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Article Citation - WoS: 18Citation - Scopus: 24Generalized Α -Meir Contraction Mappings on Branciari B-Metric Spaces(Univ Nis, Fac Sci Math, 2017) Gulyaz, Selma; Karapinar, Erdal; Erhan, Inci M.In this paper, alpha-Meir-Keeler and generalized alpha-Meir-Keeler contractions on Branciari b-metric spaces are introduced. Existence and uniqueness of fixed points of such contractions are discussed and related theorems are proved. Various consequences of the main results are also presented.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: 9Citation - Scopus: 10A Solution To Nonlinear Volterra Integro-Dynamic Equations Via Fixed Point Theory(Univ Nis, Fac Sci Math, 2019) Sevinik-Adiguzel, Rezan; Karapinar, Erdal; Erhan, Inci M.In this paper we discuss the existence and uniqueness of solutions of a certain type of nonlinear Volterra integro-dynamic equations on time scales. We investigate the problem in the setting of a complete b-metric space and apply a fixed point theorem with a contractive condition involving b-comparison function. We use the theorem to show the existence of a unique solution of some particular integro-dynamic equations.Article Citation - WoS: 27Citation - Scopus: 29Meir-Keeler Type Contractions on Modular Metric Spaces(Univ Nis, Fac Sci Math, 2018) Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; Rakocevic, VladimirIn this paper we introduce contraction mappings of Meir-Keeler types on modular metric spaces and investigate the existence and uniqueness of their fixed points. We give an example which demonstrates our theoretical results.Article Citation - WoS: 46Citation - Scopus: 43Cyclic Contractions and Fixed Point Theorems(Univ Nis, Fac Sci Math, 2012) Karapinar, Erdal; Erhan, Inci M.In this manuscript, the existence and uniqueness of fixed points of a class of cyclic operators defined on a closed subset of a Banach space is discussed. Fixed point theorems for some contractions from this class are introduced and illustrative examples are given.
