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Article Remarks on Some Coupled Fixed Point Theorems in G-Metric Spaces(2014) Agarwal, Ravi P.; Karapınar, 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 Fixed Point Theory for Cyclic (j - Ψ)-Contractions(2014) Karapınar, Erdal; Sadaranganı, KishinIn this article, the concept of cyclic (j - ψ)-contraction and a fixed point theorem for this type of mappings in the context of complete metric spaces have been presented. The results of this study extend some fixed point theorems in literature.Article A Fixed Point Theorem for Set-Valued Quasi-Contractions in B-Metric Space(2014) Karapınar, Erdal; Aydı, Hassen; Bota, Monica-felicia; Mıtrovıć, SlobodankaIn this article, we give a fixed point theorem for set-valued quasi-contraction maps in b-metric spaces. This theorem extends, unifies and generalizes several well known comparable results in the existing literature.Article Coincidence Point Theorems in Quasi-Metric Spaces Without Assuming the Mixed Monotone Property and Consequences in G-Metric Spaces(2014) Roldán, Antonio-francisco; Karapınar, 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 (α,ψ, ξ )-contractive multivalued mappings(2014) Ali, Muhammed Usman; Kamran, Tayyab; Karapınar, ErdalIn this paper, we introduce the notion of (α,ψ, ξ )-contractive multivalued mappings to generalize and extend the notion of α-ψ-contractive mappings to closed valued multifunctions. We investigate the existence of fixed points for such mappings. We also construct an example to show that our result is more general than the results of α-ψ-contractive closed valued multifunctions.
