Browsing by Author "Turkoglu, Duran"
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Article Citation Count: 18Best Approximations Theorem for a Couple in Cone Banach Space(Springer, 2010) Karapınar, Erdal; Turkoglu, Duran; MathematicsThe notion of coupled fixed point is introduced by Bhaskar and Lakshmikantham, (2006). In this manuscript, some result of Mitrovic, (2010) extended to the class of cone Banach spaces.Article Citation Count: 5A Note on 'coupled Fixed Point Theorems for Mixed g-monotone Mappings in Partially Ordered Metric Spaces'(Springer international Publishing Ag, 2014) Bilgili, Nurcan; Erhan, İnci; Erhan, Inci M.; Karapinar, Erdal; Karapınar, Erdal; Turkoglu, Duran; MathematicsRecently, some (common) coupled fixed theorems in various abstract spaces have appeared as a generalization of existing (usual) fixed point results. Unexpectedly, we noticed that most of such (common) coupled fixed theorems are either weaker or equivalent to existing fixed point results in the literature. In particular, we prove that the very recent paper of Turkoglu and Sangurlu 'Coupled fixed point theorems for mixed g-monotone mappings in partially ordered metric spaces [Fixed Point Theory and Applications 2013, 2013:348]' can be considered as a consequence of the existing fixed point theorems on the topic in the literature. Furthermore, we give an example to illustrate that the main results of Turkoglu and Sangurlu (Fixed Point Theory Appl. 2013:348, 2013) has limited applicability compared to the mentioned existing fixed point result.Article Citation Count: 26A Note on Common Fixed Points for (ψ, Α, Β)-Weakly Contractive Mappings in Generalized Metric Spaces(Springer international Publishing Ag, 2013) Bilgili, Nurcan; Karapınar, Erdal; Karapinar, Erdal; Turkoglu, Duran; MathematicsVery 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).
