Coupled fixed point theorems for generalized contractive mappings in partially ordered G-metric spaces

Abstract

In this paper, we establish some coupled coincidence and coupled common fixed point theorems for nonlinear contractive mappings having the mixed monotone property in partially ordered G-metric spaces. The results on fixed point theorems are generalizations of the recent results of Choudhury and Maity (Math.

Common coupled fixed point theorems for hybrid pair of mappings satisfying an implicit relation with application

“…Therefore, by (36), we obtain x = gx ∈ F(x, y) and y = gy ∈ F(y, x), that is, (x, y) is a common coupled fixed point of F and g. Examples 1-9 and Theorem 5 imply the following: Corollary 6 Let (X, d) be a metric space. Assume F : X × X → C B(X ) and g : X → X be mappings satisfying one of the conditions (19)- (27) of Corollary 4 and condition (28) of Theorem 5, then F and g have a coupled coincidence point.…”

“…Recently, there are several coupled fixed point results for single valued mappings established. Some instances of these works are in [6,[9][10][11]14,15,25,34,36].…”

Coupled fixed point theorems for a \phi-contractive mapping in partial metric spaces

“…Definition 2.8 [17] Let X be a non-empty set and F : X × X → X and g : X → X. We say F and g are commutative if gF (x, y) = F (gx, gy) for all x, y ∈ X. Wangkeeree and et al [28] prove coupled fixed point theorem which generalization of the result of Alsulami et al [6] as follow.…”

“…Theorem 2.9 [28] Let (X, ≤) be a partially ordered set and let there exist p be a metric on X such that (X, p) is a complete partial metric space. Let F : X × X → X be mapping having the mixed monotone property on X.…”

“…Recently, Wangkeeree and et al [28] established some coupled fixed point for generalized weakly contractive mapping having the mixed monotone property in ordered partial metric spaces.…”