Abstract
In this work, we give the notions of coupled g-coincidence point and -increasing property of F for mappings and and prove the existence and uniqueness of a coupled g-coincidence point theorem for mappings and with φ-contraction mappings in complete metric spaces without the -increasing property of F and the mixed monotone property of G. Further, we apply our results to the existence and uniqueness of a coupled g-coincidence point of the given mappings with the -increasing property of F and the mixed monotone property of H in partially ordered metric spaces.
Highlights
In, the study of a fixed point in partially ordered metric spaces was initiated by Ran and Reurings [ ], and continued by Nieto and Lopez [, ]
Afterwards, Bhaskar and Lakshmikantham [ ] introduced the concept of mixed monotone property for contractive operators in partially ordered metric spaces and proved coupled fixed point theorems for mappings which satisfy the mixed monotone property
For more work on the coupled fixed point theory and coupled coincidence point theory in partially ordered metric spaces and different spaces, we refer to the reviews
Summary
In , the study of a fixed point in partially ordered metric spaces was initiated by Ran and Reurings [ ], and continued by Nieto and Lopez [ , ]. Afterwards, Bhaskar and Lakshmikantham [ ] introduced the concept of mixed monotone property for contractive operators in partially ordered metric spaces and proved coupled fixed point theorems for mappings which satisfy the mixed monotone property.
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