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EXISTENCE OF COINCIDENCE POINT UNDER GENERALIZED NONLINEAR CONTRACTION WITH APPLICATIONS

Deshpande, Bhavana;Handa, Amrish;Thoker, Shamim Ahmad

  • Received : 2015.07.16
  • Accepted : 2016.01.12
  • Published : 2016.05.31

Abstract

We present coincidence point theorem for g-non-decreasing mappings satisfying generalized nonlinear contraction on partially ordered metric spaces. We show how multidimensional results can be seen as simple consequences of our unidimensional coincidence point theorem. We also obtain the coupled coincidence point theorem for generalized compatible pair of mappings $F,G:X^2{\rightarrow}X$ by using obtained coincidence point results. Furthermore, an example and an application to integral equation are also given to show the usability of obtained results. Our results generalize, modify, improve and sharpen several well-known results.

Keywords

Coincidence point;coupled coincidence point;generalized non-linear contraction;partially ordered metric space;O-compatible;generalized compatibility;g-non-decreasing mapping;mixed monotone mapping;commuting mapping

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