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.
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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