Common coupled fixed point theorem under weak ? ? ? contraction for hybrid pair of mappings with application

Abstract

We establish a common coupled fixed point theorem for hybrid pair of mappings under weak ? ? ? contraction on a non-complete metric space, which is not partially ordered. It is to be noted that to find coupled coincidence point, we do not employ the condition of continuity of any mapping involved therein. Moreover, an example and an application to integral equations are given here to illustrate the usability of the obtained results. We improve, extend, and generalize several known results.