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ISSN : 1226-0657

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Vol.25 No.4
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UTILIZING ISOTONE MAPPINGS UNDER GERAGHTY-TYPE CONTRACTION TO PROVE MULTIDIMENSIONAL FIXED POINT THEOREMS WITH APPLICATION

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.4, pp.279-295
https://doi.org/10.7468/jksmeb.2018.25.4.279
Deshpande, Bhavana
Handa, Amrish
Deshpande,, B. , & Handa,, A. (2018). UTILIZING ISOTONE MAPPINGS UNDER GERAGHTY-TYPE CONTRACTION TO PROVE MULTIDIMENSIONAL FIXED POINT THEOREMS WITH APPLICATION. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 25(4), 279-295, https://doi.org/10.7468/jksmeb.2018.25.4.279
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Abstract

We study the existence and uniqueness of fixed point for isotone mappings of any number of arguments under Geraghty-type contraction on a complete metric space endowed with a partial order. As an application of our result we study the existence and uniqueness of the solution to a nonlinear Fredholm integral equation. Our results generalize, extend and unify several classical and very recent related results in the literature in metric spaces.

keywords
fixed point, Geraghty-type contraction, partially ordered metric space, non-decreasing mapping, mixed monotone mapping

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

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