The underlying aim of this paper is first to state the cyclic version of J -integral Banach type contractive mappings introduced by Fallahi, Ghahramani and Soleimani Rad [Integral type contractions in partially ordered metric spaces and best proximity point, Iran. J. Sci. Technol. Trans. Sci. 44 (2020), 177-183] and second to show the existence of best proximity points for such contractive mappings in a metric space with a graph, which can entail a large number of former best proximity point results. One fundamental issue that can be distinguished between this work and previous researches is that it can also involve all of results stated by taking comparable and ϑ-close elements.
