Abstract
In this work, we prove the existence of a coupled coincidence point theorem of nonlinear contraction mappings in G-metric spaces without the mixed g-monotone property and give some examples of a nonlinear contraction mapping, which is not applied to the existence of coupled coincidence point by using the mixed monotone property. We also show the uniqueness of a coupled coincidence point of the given mapping. Further, we apply our results to the existence and uniqueness of a coupled coincidence point of the given mapping in partially ordered G-metric spaces.
Highlights
The existence of a fixed point for the contraction type of mappings in partially ordered metric spaces has been studied by Ran and Reurings [ ] and they established some new results for contractions in partially ordered metric spaces and presented applications to matrix equations
Choudhury and Maity [ ] proved the existence of a coupled fixed point theorem of nonlinear contraction mappings with mixed monotone property in partially ordered G-metric space
As a continuation of this trend, many authors have studied coupled coincidence point and coupled common fixed point results for a mixed g-monotone mapping satisfying nonlinear contractions in a partially ordered G-metric space
Summary
The existence of a fixed point for the contraction type of mappings in partially ordered metric spaces has been studied by Ran and Reurings [ ] and they established some new results for contractions in partially ordered metric spaces and presented applications to matrix equations. They gave some applications in the existence and uniqueness of the coupled fixed point theorems for mappings which satisfy the mixed monotone property.
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