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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: 4Citation - Scopus: 4Fixed Point Theorems for Generalized Weak Contractions Satisfying Rational Expression on a Ordered Partial Metric Space(Maik Nauka/interperiodica/springer, 2013) Karapinar, Erdal; Marudai, M.; Pragadeeswarar, V.The purpose of this manuscript is to present a fixed point theorem using a generalized weak contraction condition of rational type in the context of partial metric spaces.Article Citation - WoS: 9Citation - Scopus: 9Existence 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: 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: 7Citation - Scopus: 9Cyclic Contractions and Related Fixed Point Theorems on g-metric Spaces(Natural Sciences Publishing Corp-nsp, 2014) Bilgili, N.; Erhan, I. M.; Karapinar, E.; Turkoglu, D.Very recently, Jleli and Samet [53] and Samet et. al. [52] reported that some fixed point result in G-metric spaces can be derived from the fixed point theorems in the setting of usual metric space. In this paper, we prove the existence and uniqueness of fixed points of certain cyclic mappings in the context of G-metric spaces that can not be obtained by usual fixed point results via techniques used in [53,52]. We also give an example to illustrate our statements.Article Citation - Scopus: 1APPLICATIONS OF NON-UNIQUE FIXED POINT THEOREM OF CIRIC TO NONLINEAR INTEGRAL EQUATIONS(Department of Mathematics and Computer Sciences, University of Prishtina, 2019) Sevіnіk-Adigіüzel,R.; Karapinar,E.; Erhan,I.In this paper we discuss the application of the non-unique fixed point theorem of Cirić to nonlinear Fredholm integral equations. We establish an existence theorem for the solutions of such integral equations and apply the theorem to particular examples. © 2019 Universiteti i Prishtinës, Prishtinë, Kosovë.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: 49On Fixed Point Results for Α-Implicit Contractions in Quasi-Metric Spaces and Consequences(inst Mathematics & informatics, 2016) Aydi, Hassen; Jellali, Manel; Karapinar, ErdalIn this paper, we prove some fixed point results involving alpha-implicit contractions in quasi-metric spaces. Moreover, we provide some known results on G-metric spaces. An example and an application on a solution of a nonlinear integral equation are also presented.
