Common Coupled Fixed Point Theorems without Compatibility in Partially Ordered Metric Spaces

Abstract

A perfect blend of requirements for the proof of common coupled fixed point theorems in partially ordered metric space without the assumptions of (weak) compatibility is accomplished. Previous attempts in this direction involving these assumptions mostly ensure existence of coupled coincidence points. In many existing works in this area, attempt have been made to prove the existence of common coupled fixed points. However, only identity mappings can satisfy the conditions of the theorems. The method of proof presented in this present work is powerful in view of the fact that it guarantees the existence of common coupled fixed points
without the imposition of (weak) compatibility conditions and identity mappings. To illustrate the results, an example is provided.