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Article Citation - Scopus: 29Fixed Point Theorem on Partial Metric Spaces Involving Rational Expressions(University of Miskolc, 2013) Karapinar,E.; Shatanawi,W.; Tas,K.We establish a fixed point theorem involving a rational expression in a complete partial metric space. Our result generalizes a well-known result in (usual) metric spaces. Also, we introduce an example to illustrate the usability of our result. © Miskolc University Press.Article Citation - Scopus: 71A Note on Common Fixed Point Theorems in Partial Metric Spaces(University of Miskolc, 2011) Karapinar,E.In this manuscript, we consider the notion of generalized Sehgal contraction condition in a partial metric space. For the pair of two self mappings (S, T) which satisfies Sehgal contraction condition, we obtain a unique common fixed point. © 2011 Miskolc University Press.Article Citation - Scopus: 62Weak ø-Contraction on partial metric spaces(2012) Karapinar,E.In this manuscript, the notion of weak ø-contraction is considered on partial metric space. It is shown that a self mapping T on a complete partial metric space X has a fixed point if they satisfied weak ø-contraction. © 2012 EUDOXUS PR20E6SS, LLC.Article Citation - WoS: 199Citation - Scopus: 195Existence and uniqueness of a common fixed point on partial metric spaces(Pergamon-elsevier Science Ltd, 2011) Abdeljawad, T.; Karapinar, E.; Tas, K.In this work, a general form of the weak phi-contraction is considered on partial metric spaces, to get a common fixed point. It is shown that self-mappings S, T on a complete partial metric space X have a common fixed point if it is a generalized weak phi-contraction. (C) 2011 Elsevier Ltd. All rights reserved.Article Citation - WoS: 79Citation - Scopus: 82A Generalized Contraction Principle With Control Functions on Partial Metric Spaces(Pergamon-elsevier Science Ltd, 2012) Abdeljawad, Thabet; Karapinar, Erdal; Tas, KenanPartial metric spaces were introduced by Matthews in 1994 as a part of the study of denotational semantics of data flow networks. In this article, we prove a generalized contraction principle with control functions phi and psi on partial metric spaces. The theorems we prove generalize many previously obtained results. We also give some examples showing that our theorems are indeed proper extensions. (C) 2011 Elsevier Ltd. All rights reserved.Article Citation - WoS: 74Citation - Scopus: 74Fixed Point Theorems on Quasi-Partial Metric Spaces(Pergamon-elsevier Science Ltd, 2013) Karapinar, Erdal; Erhan, I. M.; Ozturk, AliIn this paper, the concept of a quasi-partial metric space is introduced, and some general fixed point theorems in quasi-partial metric spaces are proved. (C) 2012 Elsevier Ltd. All rights reserved.Article Citation - Scopus: 15Some Fixed Point Theorems on the Class of Comparable Partial Metric Spaces(2011) Karapinar,E.In this paper we present existence and uniqueness criteria of a fixed point for a self mapping on a non-empty set endowed with two comparable partial metrics. © Universidad Politécnica de Valencia.Article Citation - WoS: 142Citation - Scopus: 138Generalizations of Caristi Kirk's Theorem on Partial Metric Spaces(Springer international Publishing Ag, 2011) Karapinar, ErdalIn this article, lower semi-continuous maps are used to generalize Cristi-Kirk's fixed point theorem on partial metric spaces. First, we prove such a type of fixed point theorem in compact partial metric spaces, and then generalize to complete partial metric spaces. Some more general results are also obtained in partial metric spaces. 2000 Mathematics Subject Classification 47H10,54H25Article Citation - Scopus: 22On Ekeland's Variational Principle in Partial Metric Spaces(Natural Sciences Publishing Co., 2015) Aydi,H.; Karapinar,E.; Vetro,C.In this paper, lower semi-continuous functions are used to extend Ekeland's variational principle to the class of partial metric spaces. As consequences of our results, we obtain some fixed point theorems of Caristi and Clarke types. © 2015 NSP.Article Citation - WoS: 63Citation - Scopus: 61Fixed Point Theorem for Cyclic Maps on Partial Metric Spaces(Natural Sciences Publishing Corp-nsp, 2012) Karapinar, E.; Erhan, I. M.; Ulus, A. Yildiz; MathematicsIn this paper, a class of cyclic contractions on partial metric spaces is introduced. A fixed point theorem for cyclic contractions on partial metric spaces satisfying (psi, phi) contractive condition, and illustrative examples are given.
