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Article Citation - WoS: 9Citation - Scopus: 8Existence and Uniqueness of Best Proximity Points Under Rational Contractivity Conditions(Walter de Gruyter Gmbh, 2016) Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-Francisco; Sadarangani, KishinThe main aim of this paper is to present some theorems in order to guarantee existence and uniqueness of best proximity points under rational contractivity conditions using very general test functions. To illustrate the variety of possible test functions, we include some examples of pairs of functions which are included in innovative papers published in the last years. As a consequence, we prove that our results unify and extend some recent results in this field.Article Citation - WoS: 63Citation - Scopus: 75Α-Ψ Contraction Type Mappings and Some Related Fixed Point Results(Univ Nis, Fac Sci Math, 2014) Karapinar, ErdalIn this paper, we consider a generalization of alpha-psi-Geraghty contractions and investigate the existence and uniqueness of fixed point for the mapping satisfying this condition. We illustrate an example and an application to support our results. In particular, we extend, improve and generalize some earlier results in the literature on this topic.Article Citation - WoS: 23Citation - Scopus: 31A Discussion on "α-Ψ Contraction Type Mappings "(Univ Nis, Fac Sci Math, 2014) Karapinar, ErdalIn this paper we discuss the subadditivity property of some auxiliary functions which have been used to generalize the contractive conditions on maps. Our results show that this property is not required in many cases and therefore, can be removed. We emphasize that in several papers (see e.g.[1]-[11]) dealing with such contraction mappings, the hypotheses of the main theorems can be restated in the light of our results.Article Citation - WoS: 88Citation - Scopus: 97Modified f-contractions Via α-admissible Mappings and Application To Integral Equations(Univ Nis, Fac Sci Math, 2017) Aydi, Hassen; Karapinar, Erdal; Yazidi, HabibIn this paper, we introduce the concept of a modified F-contraction via alpha-admissible mappings and propose some theorems that guarantee the existence and uniqueness of fixed point for such mappings in the frame of complete metric spaces. We also provide some illustrative examples. Moreover, we consider an application solving an integral equation.Article Citation - WoS: 21Citation - Scopus: 27Some Fixed-Point Theorems in b-Dislocated Metric Space and Applications(Mdpi, 2018) Kumari, Panda Sumati; Alqahtani, Obaid; Karapinar, ErdalIn this article, we prove some fixed-point theorems in b-dislocated metric space. Thereafter, we propose a simple and efficient solution for a non-linear integral equation and non-linear fractional differential equations of Caputo type by using the technique of fixed point.Article Citation - WoS: 6Citation - Scopus: 10On Quasi-Contraction Mappings of Ciric and Fisher Type Via ω-distance(Natl inquiry Services Centre Pty Ltd, 2019) Darko, Kocev; Karapinar, Erdal; Rakocevic, VladimirKada, Suzuki, and Takahashi introduced and studies the concept of omega- distance in fixed point theory. In this paper, we generalize and unify Ciric' and Fisher fixed points results for quasi-contractions on metric space to omega-distance on complete metric spaces. We also extend some results of Kada, Suzuki and Takahashi, and Suzuki. Our methods of proofs are new and even simpler than the corresponding methods in 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: 14Citation - Scopus: 13SOME FIXED POINT THEOREMS IN BRANCIARI METRIC SPACES(Walter de Gruyter Gmbh, 2017) Berzig, Maher; Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio F.In this paper, we investigate the existence and uniqueness of a fixed point of certain contraction via auxiliary functions in the context of complete Branciari metric spaces endowed with a transitive binary relation. Our results unify and extend some existing fixed point results in the related literature.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: 103Citation - Scopus: 108On Generalized Α - Ψ-Geraghty Contractions on b-metric Spaces(Walter de Gruyter Gmbh, 2020) Afshari, Hojjat; Aydi, Hassen; Karapinar, ErdalIn this paper, we consider generalized alpha - psi-Geraghty contractive type mappings and investigate the existence and uniqueness of a fixed point for mappings involving such contractions. In particular, we extend, improve and generalize some earlier results in the literature on this topic. An application concerning the existence of an integral equation is also considered to illustrate the novelty of the main result.
