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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: 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: 48Citation - Scopus: 45Fixed Point Results for gm< Contractive and g-(α, Ψ)-Meir Contractive Mappings(Springer international Publishing Ag, 2013) Hussain, Nawab; Karapinar, Erdal; Salimi, Peyman; Vetro, PasqualeIn this paper, first we introduce the notion of a G(m)-Meir-Keeler contractive mapping and establish some fixed point theorems for the G(m)-Meir-Keeler contractive mapping in the setting of G-metric spaces. Further, we introduce the notion of a G(c)(m)-Meir-Keeler contractive mapping in the setting of G-cone metric spaces and obtain a fixed point result. Later, we introduce the notion of a G-(alpha, psi)-Meir-Keeler contractive mapping and prove some fixed point theorems for this class of mappings in the setting of G-metric spaces.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: 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.
