COMMON COUPLED FIXED POINT THEOREM UNDER WEAK ψ − ϕ CONTRACTION FOR HYBRID PAIR OF MAPPINGS WITH APPLICATION

BHAVANA DESHPANDE, AMRISH HANDA, LAKSHMI NARAYAN MISHRA

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Abstract

We establish a common coupled fixed point theorem for hybrid pair of mappings under weak ψ − ϕ contraction on a non-complete metric space, which is not partially ordered. It is to be noted that to nd 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.

Keywords

Coupled fixed point, coupled coincidence point, weak ψ − ϕ contraction, w-compatibility, F-weakly commuting mappings.