UTILIZING ISOTONE MAPPINGS UNDER GERAGHTY-TYPE CONTRACTION TO PROVE MULTIDIMENSIONAL FIXED POINT THEOREMS WITH APPLICATION

한국수학교육학회지시리즈B:순수및응용수학 / 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 (Department of Mathematics, Govt. P. G. Arts and Science College)
Handa, Amrish (Department of Mathematics, Govt. P. G. Arts and Science College)

Deshpande, Bhavana, & Handa, Amrish. (2018). UTILIZING ISOTONE MAPPINGS UNDER GERAGHTY-TYPE CONTRACTION TO PROVE MULTIDIMENSIONAL FIXED POINT THEOREMS WITH APPLICATION. 한국수학교육학회지시리즈B:순수및응용수학, 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

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논문 상세

Vol.25 No.4

UTILIZING ISOTONE MAPPINGS UNDER GERAGHTY-TYPE CONTRACTION TO PROVE MULTIDIMENSIONAL FIXED POINT THEOREMS WITH APPLICATION

UTILIZING ISOTONE MAPPINGS UNDER GERAGHTY-TYPE CONTRACTION TO PROVE MULTIDIMENSIONAL FIXED POINT THEOREMS WITH APPLICATION

Abstract

한국수학교육학회지시리즈B:순수및응용수학