Coupled fixed points results for w-compatible maps in symmetric G-metric spaces

Sumitra Dalal, Sunny Chauhan

Abstract


Mustafa et. al [21] generalized the concept of metric space by introducing G-metric space and proved fixed point theorems for mappings satisfying different contractive conditions [see,21-27]. In this article, we introduce the notion of w-compatible maps, b-coupled coincidence points and b-common coupled fixed points for non self maps and obtain fixed point results using these new notions in G-metric spaces. It is worth to mention that our results neither rely on completeness of the space nor the continuity of any mappings involved therein. Also, relevant examples have been cited to illustrate the effectiveness of our results. As an application, we demonstrate the existence of solution of system of non linear integral equations. Our work sets analogues, unifies, generalizes, extends and improves several well known results existing in literature, in particular the recent results of [1-5,8,9,19,20] etc. in the frame work of G-metric spaces.


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References


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