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ISSN : 1226-0657

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Vol.25 No.2

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EMPLOYING α-ψ-CONTRACTION TO PROVE COUPLED COINCIDENCE POINT THEOREM FOR GENERALIZED COMPATIBLE PAIR OF MAPPINGS ON PARTIALLY ORDERED METRIC SPACES

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
2018, v.25 no.2, pp.73-94
https://doi.org/10.7468/jksmeb.2018.25.2.73
Deshpande, Bhavana
Handa, Amrish
Deshpande,, B. , & Handa,, A. (2018). EMPLOYING α-ψ-CONTRACTION TO PROVE COUPLED COINCIDENCE POINT THEOREM FOR GENERALIZED COMPATIBLE PAIR OF MAPPINGS ON PARTIALLY ORDERED METRIC SPACES. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 25(2), 73-94, https://doi.org/10.7468/jksmeb.2018.25.2.73

Abstract

We introduce some new type of admissible mappings and prove a coupled coincidence point theorem by using newly defined concepts for generalized compatible pair of mappings satisfying <TEX>${\alpha}-{\psi}$</TEX> contraction on partially ordered metric spaces. We also prove the uniqueness of a coupled fixed point for such mappings in this setup. Furthermore, we give an example and an application to integral equations to demonstrate the applicability of the obtained results. Our results generalize some recent results in the literature.

keywords
coupled coincidence point, <tex> ${\alpha}-{\psi}$</tex> contraction, generalized compatibility, increasing mapping, mixed monotone mapping, commuting mapping

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

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