ON COMMON COUPLED FIXED POINT THEOREMS WITHOUT COMPATIBILITY IN PARTIALLY ORDERED PARTIAL METRIC SPACES WITH APPLICATIONS

Abstract

In this paper, we prove common coupled fixed point theorems for rational typecontractive condition in the setting of partially ordered complete partial metric spaces with-out the assumption of (weak) compatibility. In many existing works in this direction, attempthave been made to prove the existence of common coupled points. However, only identitymappings can satisfy the conditions of the theorems. The method of proof presented in thiswork is powerful and it guarantees the existence of common coupled fixed points without using the (weak) compatibility conditions and identity mappings. In addition, we provide someconsequences of the established results. To illustrate the results, an example is provided.Also, we give some applications of the result in terms of integral type contractions. Ourresults extend and generalize several previously published results from the existing literature(see, e.g., [41]).