Abstract
In this paper, we use the notion of a mixed weakly monotone pair of maps of Gordji et al. (Fixed Point Theory Appl. 2012:95, 2012) to state a coupled common fixed point theorem for maps on partially ordered S-metric spaces. This result generalizes the main results of Gordji et al. (Fixed Point Theory Appl. 2012:95, 2012), Bhaskar, Lakshmikantham (Nonlinear Anal. 65(7):1379-1393, 2006), Kadelburg et al. (Comput. Math. Appl. 59:3148-3159, 2010) into the structure of S-metric spaces.
Highlights
Introduction and preliminariesThere are many generalized metric spaces such as -metric spaces [ ], G-metric spaces [ ], D*-metric spaces [ ], partial metric spaces [ ] and cone metric spaces [ ]
In [ ], Sedghi, Shobe and Aliouche have introduced the notion of an S-metric space and proved that this notion is a generalization of a G-metric space and a D*-metric space. They have proved some properties of S-metric spaces and some fixed point theorems for a self-map on an S-metric space
In [ ], Gordji et al have introduced the concept of a mixed weakly monotone pair of maps and proved some coupled common fixed point theorems for a contractive-type maps with the mixed weakly monotone property in partially ordered metric spaces
Summary
Introduction and preliminariesThere are many generalized metric spaces such as -metric spaces [ ], G-metric spaces [ ], D*-metric spaces [ ], partial metric spaces [ ] and cone metric spaces [ ]. They have proved some properties of S-metric spaces and some fixed point theorems for a self-map on an S-metric space. In [ ], Gordji et al have introduced the concept of a mixed weakly monotone pair of maps and proved some coupled common fixed point theorems for a contractive-type maps with the mixed weakly monotone property in partially ordered metric spaces.
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