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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: 46Citation - Scopus: 49Fixed Point Theorems for Generalized (α* - Ψ)-Ciric Contractive Multivalued Operators in b-metric Spaces(int Scientific Research Publications, 2016) Bota, Monica-Felicia; Chifu, Cristian; Karapinar, ErdalIn this paper we introduce the notion (alpha(*) - psi)- Ciric-type contractive multivalued operator and investigate the existence and uniqueness of fixed point for such a mapping in b-metric spaces. The well-posedness of the fixed point problem and the Ulam-Hyres stability is also studied. (C) 2016 All rights reserved.Article Citation - WoS: 5Citation - Scopus: 14Existence of a Solution of Integral Equations Via Fixed Point Theorem(Springeropen, 2013) Gulyaz, Selma; Karapinar, Erdal; Rakocevic, Vladimir; Salimi, PeymanIn this paper, we establish a solution to the following integral equation: u(t) = integral(T)(0) G(t, s)f(s, u(s)) ds for all t is an element of [0,T], (1) where T > 0, f : [0, T] x R -> R and G : [0, T] x [0, T] -> [0, infinity) are continuous functions. For this purpose, we also obtain some auxiliary fixed point results which generalize, improve and unify some fixed point theorems in the literature.Article Citation - WoS: 77Citation - Scopus: 81α-admissible mappings and related fixed point theorems(Springeropen, 2013) Hussain, Nawab; Karapinar, Erdal; Salimi, Peyman; Akbar, FarhanaIn this paper, we prove the existence and uniqueness of a fixed point for certain alpha-admissible contraction mappings. Our results generalize and extend some well-known results on the topic in the literature. We consider some examples to illustrate the usability of our results.Article Citation - WoS: 13Citation - Scopus: 18On the existence of fixed points that belong to the zero set of a certain function(Springer international Publishing Ag, 2015) Karapinar, Erdal; O'Regan, Donal; Samet, BessemLet T : X -> X be a given operator and F-T be the set of its fixed points. For a certain function phi : X -> [0,infinity), we say that F-T is phi-admissible if F-T is nonempty and F-T subset of Z(phi), where Z(phi) is the zero set of phi. In this paper, we study the phi-admissibility of a new class of operators. As applications, we establish a new homotopy result and we obtain a partial metric version of the Boyd-Wong fixed point theorem.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: 60Citation - Scopus: 72Remarks on some coupled fixed point theorems in G-metric spaces(Springer international Publishing Ag, 2013) Agarwal, Ravi P.; Karapinar, ErdalIn this paper, we show that, unexpectedly, most of the coupled fixed point theorems in the context of (ordered) G-metric spaces are in fact immediate consequences of usual fixed point theorems that are either well known in the literature or can be obtained easily.Article Citation - WoS: 57Citation - Scopus: 71Fixed Point Theorems for Α-Geraghty Contraction Type Maps in Metric Spaces(Springer int Publ Ag, 2013) Cho, Seong-Hoon; Bae, Jong-Sook; Karapinar, ErdalIn this paper, we introduce a notion of alpha-Geraghty contraction type maps in the setting of a metric space. We also establish some fixed point theorems for such maps and give an example to illustrate our results. Finally, we discuss the application of our main results in the research fields of ordinary differential equations.Article Citation - WoS: 4Citation - Scopus: 5A Note on '(g, f)-closed Set and Tripled Point of Coincidence Theorems for Generalized Compatibility in Partially Metric Spaces'(Springeropen, 2014) Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-FranciscoRecently, some (common) multidimensional fixed theorems in partially ordered complete metric spaces have appeared as a generalization of existing (usual) fixed point results. Unexpectedly, we realized 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 results included in the very recent paper (Charoensawan and Thangthong in Fixed Point Theory Appl. 2014:245, 2014) can be considered as a consequence of existing fixed point theorems on the topic in the literature.Article Citation - WoS: 92Citation - Scopus: 101Modified 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.
