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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: 201Citation - Scopus: 263On α-ψ< Contractive Mappings(Springer international Publishing Ag, 2013) Karapinar, Erdal; Kumam, Poom; Salimi, PeymanIn this paper, we introduce the notion of alpha-psi-Meir-Keeler contractive mappings via a triangular alpha-admissible mapping. We discuss the existence and uniqueness of a fixed point of such a mapping in the setting of complete metric spaces. We state a number of examples to illustrate our results. MSC: 46N40, 47H10, 54H25, 46T99.Article Citation - WoS: 15Citation - Scopus: 15A Note on 'ψ-geraghty Type Contractions'(Springer international Publishing Ag, 2014) Karapinar, Erdal; Samet, BessemVery recently, the notion of a psi-Geraghty type contraction was defined by Gordji et al. (Fixed Point Theory and Applications 2012: 74, 2012). In this short note, we realize that the main result via psi-Geraghty type contraction is equivalent to an existing related result in the literature. Consequently, all results inspired by the paper of Gordji et al. in (Fixed Point Theory and Applications 2012:74, 2012) can be derived in the same way.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: 13Citation - Scopus: 19A Note on Caristi-Type Cyclic Maps: Related Results and Applications(Springer international Publishing Ag, 2013) Du, Wei-Shih; Karapinar, ErdalIn this note, we first introduce the concept of Caristi-type cyclic map and present a new convergence theorem and a best proximity point theorem for Caristi-type cyclic maps. It should be mentioned that in our results, the dominated functions need not possess the lower semicontinuity property. Some best proximity point results and convergence theorems in the literature have been derived from our main results. Consequently, the presented results improve, extend and generalize some of the existence results on the topic.Article Citation - WoS: 28Citation - Scopus: 33Coincidence Point Theorems in Quasi-Metric Spaces Without Assuming the Mixed Monotone Property and Consequences in g-metric Spaces(Springer international Publishing Ag, 2014) Roldan-Lopez-de-Hierro, Antonio-Francisco; Karapinar, Erdal; de la Sen, ManuelIn this paper, we present some coincidence point theorems in the setting of quasi-metric spaces that can be applied to operators which not necessarily have the mixed monotone property. As a consequence, we particularize our results to the field of metric spaces, partially ordered metric spaces and G-metric spaces, obtaining some very recent results. Finally, we show how to use our main theorems to obtain coupled, tripled, quadrupled and multidimensional coincidence point results.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: 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.
