A Note on 'coupled Fixed Point Theorems for Mixed <i>g</I>-monotone Mappings in Partially Ordered Metric Spaces'
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Date
2014
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Springer international Publishing Ag
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Abstract
Recently, 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.
Description
KARAPINAR, ERDAL/0000-0002-6798-3254; ERHAN, INCI M./0000-0001-6042-3695
Keywords
fixed point, G-metric space, cyclic maps, cyclic contractions