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http://dx.doi.org/10.7468/jksmeb.2018.25.4.279

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

Deshpande, Bhavana (Department of Mathematics, Govt. P. G. Arts and Science College)
Handa, Amrish (Department of Mathematics, Govt. P. G. Arts and Science College)
Publication Information
The Pure and Applied Mathematics / v.25, no.4, 2018 , pp. 279-295 More about this Journal
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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