The purpose of this work is to present some existence theorems for coupled fixed points of F -type contractive operator in metric spaces endowed with a directed graph. Our results generalize the main result obtained by Chifu and Petrusel [C. Chifu, G. Petrusel, Fixed Point Theory Appl., 2014 (2014), 13 pages]. We also present applications to some nonlinear integral system equations to support the results. c 2016 all rights reserved.
Inspired by the work of Dakjum et al. [Eshi, D., Das, P. K. and Debnath, P., Coupled coincidence and coupled common fixed point theorems on a metric space with a graph, Fixed Point Theory Appl., 37 (2016), 1–14], we introduce a new class of G − f−contraction mappings in complete fuzzy metric spaces endowed with a directed graph and prove some existence results for coupled coincidence and coupled common fixed point theorems of this type of contraction mappings in complete fuzzy metric spaces endowed with a directed graph.
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