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COMMON COUPLED FIXED POINT THEOREM UNDER GENERALIZED MIZOGUCHI-TAKAHASHI CONTRACTION FOR HYBRID PAIR OF MAPPINGS GENERALIZED MIZOGUCHI-TAKAHASHI CONTRACTION

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2015, v.22 no.3, pp.199-214
https://doi.org/10.7468/jksmeb.2015.22.3.199
DESHPANDE, BHAVANA
HANDA, AMRISH

Abstract

We establish a common coupled fixed point theorem for hybrid pair of mappings under generalized Mizoguchi-Takahashi contraction on a noncomplete metric space, which is not partially ordered. It is to be noted that to find coupled oincidence point, we do not employ the condition of continuity of any mapping involved therein. An example is also given to validate our results. We improve, extend and generalize several known results.

keywords
coupled fixed point, coupled coincidence point, generalized Mizoguchi-Takahashi contraction, w−compatibility, F−weakly commutativity.

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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics