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Article Citation - WoS: 91Citation - Scopus: 109New Extension of p-metric Spaces With Some Fixed-Point Results on m-metric Spaces(Springer international Publishing Ag, 2014) Asadi, Mehdi; Karapinar, Erdal; Salimi, PeymanIn this paper, we extend the p-metric space to an M-metric space, and we shall show that the definition we give is a real generalization of the p-metric by presenting some examples. In the sequel we prove some of the main theorems by generalized contractions for getting fixed points and common fixed points for mappings.Article Citation - WoS: 7A New Fixed Point Result Via Property P With an Application(int Scientific Research Publications, 2017) Mustafa, Zead; Jaradat, M. M. M.; Karapinar, ErdalThe purpose of this paper is to introduce a new contractive condition. We prove the existence and uniqueness of a fixed point of self-mapping under this new contractive condition. Moreover, we observe analog of these results for the mappings that satisfy the property P. An application on integral equations is presented to illustrate the main result. Our results extend and generalize well-known results in the literature. (C) 2017 All rights reserved.Article Citation - WoS: 35Fixed Point Theorem on Partial Metric Spaces Involving Rational Expressions(Univ Miskolc inst Math, 2013) Karapinar, Erdal; Shatanawi, Wasfi; Tas, KenanWe 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.Article Citation - WoS: 54WEAK φ-CONTRACTION ON PARTIAL METRIC SPACES(Eudoxus Press, Llc, 2012) Karapinar, ErdalIn this manuscript, the notion of weak phi-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 phi-contraction.Article Citation - WoS: 3Citation - Scopus: 5Fixed Point Theorems for Generalized Contractions on gp-metric Spaces(Springeropen, 2013) Bilgili, Nurcan; Karapinar, Erdal; Salimi, PeymanIn this paper, we present two fixed point theorems on mappings, defined on GP-complete GP-metric spaces, which satisfy a generalized contraction property determined by certain upper semi-continuous functions. Furthermore, we illustrate applications of our theorems with a number of examples. Inspired by the work of Jachymski, we also establish equivalences of certain auxiliary maps in the context of GP-complete GP-metric spaces. MSC: 47H10, 54H25.Article Citation - WoS: 29Citation - Scopus: 44Fixed Points of Conditionally f-contractions in Complete Metric-Like Spaces(Springer international Publishing Ag, 2015) Karapinar, Erdal; Kutbi, Marwan A.; Piri, Hossein; O'Regan, DonalIn this paper, we introduce the notion of a conditionally F-contraction in the setting of complete metric-like spaces and we investigate the existence of fixed points of such mappings. Our results unify, extend, and improve several results in the literature.Article Citation - WoS: 31Citation - Scopus: 36Nonunique Fixed Point Theorems in Partial Metric Spaces(Univ Nis, Fac Sci Math, 2013) Karapinar, Erdal; Romaguera, SalvadorIn this paper we prove the existence of fixed points of certain self-maps in the context of partial metric spaces. In fact, the fixed point theorems presented here can be considered as a continuation, in part, of the works of L. B. Ciric on the existence of fixed points but not uniqueness in the realm of metric spaces. Our results generalize, enrich and improve earlier results on the topic in the literature.Article Citation - WoS: 28Citation - Scopus: 34A Note on Common Fixed Points for (ψ, Α, Β)-Weakly Contractive Mappings in Generalized Metric Spaces(Springer international Publishing Ag, 2013) Bilgili, Nurcan; Karapinar, Erdal; Turkoglu, DuranVery recently, Isik and Turkoglu (Fixed Point Theory Appl. 2013:131, 2013) proved a common fixed point theorem in a rectangular metric space by using three auxiliary distance functions. In this paper, we note that this result can be derived from the recent paper of Lakzian and Samet (Appl. Math. Lett. 25:902-906, 2012).Article Citation - WoS: 68A Note on Common Fixed Point Theorems in Partial Metric Spaces(Univ Miskolc inst Math, 2011) Karapinar, ErdalIn 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.Article Citation - WoS: 19Citation - Scopus: 24Fixed Point Results for the Α-Meir Contraction on Partial Hausdorff Metric Spaces(Springeropen, 2013) Chen, Chi-Ming; Karapinar, ErdalThe purpose of this paper is to study fixed point theorems for a multi-valued mapping satisfying the alpha-Meir-Keeler contraction with respect to the partial Hausdorff metric H in complete partial metric spaces. Our result generalizes and extends some results in the literature.
