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Common fixed point results in metric spaces endowed with a graph -by Binayak S. Choudhury, Nikhilesh Metiya, Debashis Khatua

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Abstract: In this paper we establish some common fixed point results for a pair of mappings in a metric space having the additional structure of a directed graph. The mappings are assumed to satisfy certain almost $G$-contractions without and with rational terms. Each of our results is illustrated with example. The approach here is a blending of analytic and graph theoretic methodologies.

Keywords: Metric space,  directed graph,  $G$-contraction and common fixed point.

DOI: https://doi.org/10.30697/rfpta-2018-18

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How to cite this article: Binayak S. Choudhury, Nikhilesh Metiya, Debashis Khatua, Common fixed point results in metric spaces endowed with a graph, Results in Fixed Point Theory and Applications, vol. 2018, Article ID 201818, 8 pages, 2018.

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Copyright © 2018 SUMA Publishing Group., This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.