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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: 21Citation - Scopus: 23Best Proximity Points of Generalized Almost Ψ-Geraghty Contractive Non-Self(Springer international Publishing Ag, 2014) Aydi, Hassen; Karapinar, Erdal; Erhan, Inci M.; Salimi, PeymanIn 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.Article Citation - WoS: 16Citation - Scopus: 18Weak Ψ-Contractions on Partially Ordered Metric Spaces and Applications To Boundary Value Problems(Springeropen, 2014) Karapinar, Erdal; Erhan, Inci M.; Aksoy, UmitA class of weak psi-contractions satisfying the C-condition is defined on metric spaces. The existence and uniqueness of fixed points of such maps are discussed both on metric spaces and on partially ordered metric spaces. The results are applied to a first order periodic boundary value problem.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: 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: 6Citation - Scopus: 5A Note on 'coupled Fixed Point Theorems for Mixed g-monotone Mappings in Partially Ordered Metric Spaces'(Springer international Publishing Ag, 2014) Bilgili, Nurcan; Erhan, Inci M.; Karapinar, Erdal; Turkoglu, DuranRecently, some (common) coupled fixed theorems in various abstract spaces have appeared as a generalization of existing (usual) fixed point results. Unexpectedly, we noticed that most of such (common) coupled fixed theorems are either weaker or equivalent to existing fixed point results in the literature. In particular, we prove that the very recent paper of Turkoglu and Sangurlu 'Coupled fixed point theorems for mixed g-monotone mappings in partially ordered metric spaces [Fixed Point Theory and Applications 2013, 2013:348]' can be considered as a consequence of the existing fixed point theorems on the topic in the literature. Furthermore, we give an example to illustrate that the main results of Turkoglu and Sangurlu (Fixed Point Theory Appl. 2013:348, 2013) has limited applicability compared to the mentioned existing fixed point result.Article Citation - WoS: 3Citation - Scopus: 5A Fixed Point Theorem for Meir-Keeler Type Contraction Via Gupta-Saxena Expression(Springer international Publishing Ag, 2015) Redjel, Najeh; Dehici, Abdelkader; Erhan, Inci M.In this paper, following the idea of Samet et al. (J. Nonlinear. Sci. Appl. 6: 162-169, 2013), we establish a new fixed point theorem for a Meir-Keeler type contraction via Gupta-Saxena rational expression which enables us to extend and generalize their main result (Gupta and Saxena in Math. Stud. 52: 156-158, 1984). As an application we derive some fixed points of mappings of integral type.Article Citation - WoS: 24Citation - Scopus: 5Remarks on 'Coupled coincidence point results for a generalized compatible pair with applications'(Springer international Publishing Ag, 2014) Erhan, Inci M.; Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-Francisco; Shahzad, NaseerVery recently, Hussain et al. (Fixed Point Theory Appl. 2014:62, 2014) announced the existence and uniqueness of some coupled coincidence point. In this short note we remark that the announced results can be derived from the coincidence point results in the literature.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: 18Some fixed point theorems for (α, ψ)-rational type contractive mappings(Springer international Publishing Ag, 2015) Alsulami, Hamed H.; Chandok, Sumit; Taoudi, Mohamed-Aziz; Erhan, Inci M.In this paper, we introduce the concept of (alpha, psi)-rational type contractive mappings and provide sufficient conditions for the existence and uniqueness of a fixed point for such class of generalized nonlinear contractive mappings in the setting of generalized metric spaces. We also deduce several interesting corollaries.
