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Article Citation - WoS: 8Citation - Scopus: 11g-metric Spaces in Any Number of Arguments and Related Fixed-Point Theorems(Springer international Publishing Ag, 2014) Roldan, Antonio; Karapinar, Erdal; Kumam, PoomInspired by the notion of Mustafa and Sims' G-metric space and the attention that this kind of metric has received in recent times, we introduce the concept of a G-metric space in any number of variables, and we study some of the basic properties. Then we prove that the family of this kind of metric is closed under finite products. Finally, we show some fixed-point theorems that improve and extend some well-known results in this field.Article Citation - WoS: 15Contractive Multivalued Maps in Terms of q-functions on Complete Quasimetric Spaces(Springer international Publishing Ag, 2014) Karapinar, Erdal; Romaguera, Salvador; Tirado, PedroIn this paper we prove the existence of a fixed point for multivalued maps satisfying a contraction condition in terms of Q-functions, and via Bianchini-Grandolfi gauge functions, for complete T-0-quasipseudometric spaces. Our results extend, improve, and generalize some recent results in the literature. We present some examples to validate and illustrate our results.Article Citation - WoS: 61Citation - Scopus: 81Dislocated metric space to metric spaces with some fixed point theorems(Springer international Publishing Ag, 2013) Karapinar, Erdal; Salimi, PeymanIn this paper, we notice the notions metric-like space and dislocated metric space are exactly the same. After this historical remark, we discuss the existence and uniqueness of a fixed point of a cyclic mapping in the context of metric-like spaces. We consider some examples to illustrate the validity of the derived results of this paper.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: 31Citation - Scopus: 43On Best Proximity Point of Ψ-Geraghty Contractions(Springer international Publishing Ag, 2013) Karapinar, ErdalVery recently, Caballero, Harjani and Sadarangani (Fixed Point Theory Appl. 2012: 231, 2012) observed some best proximity point results for Geraghty contractions by using the P-property. In this paper, we introduce the notion of psi-Geraghty contractions and show the existence and uniqueness of the best proximity point of such contractions in the setting of a metric space. We state examples to illustrate our result.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: 25Citation - Scopus: 32Remarks on Some Recent Fixed Point Theorems(Springer international Publishing Ag, 2012) Aydi, Hassen; Karapinar, Erdal; Samet, BessemThe purpose of this article is to show that some recent fixed point theorems are particular results of previous existing theorems in the literature. Mathematics Subject Classification 2000: 54H25; 47H10.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: 93Citation - Scopus: 111New 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: 78Citation - Scopus: 63Discussion on Some Coupled Fixed Point Theorems(Springer international Publishing Ag, 2013) Samet, Bessem; Karapinar, Erdal; Aydi, Hassen; Rajic, Vesna CojbasicIn this paper, we show that, unexpectedly, most of the coupled fixed point theorems (on ordered metric spaces) are in fact immediate consequences of well-known fixed point theorems in the literature. MSC: 47H10, 54H25.
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