Coupled and Common Coupled Fixed Point Theorems Under New Coupled Implicit Relation in Partial Metric Spaces

The purpose of this paper is to study existence and uniqueness of coupledand common coupled fixed point theorems for self-mappings satisfying a new coupledimplicit relation in the setting of partial metric spaces and give some corollaries ofTheorem 3.1. Furthermore, we prove well-posedness of a coupled fixed point problem.We also provide some applications of our result to a mapping with a contraction ofintegral type. The results of findings in this paper extend and generalize several resultsfrom the existing literature.