Graphical cyclic $\mathcal{J}$-integral Banach type mappings and the existence of their best proximity points
Subject Areas : Operator theory
1 - Department of Mathematics, Payame Noor University, Tehran, Iran
2 - Department of Mathematics, Payame Noor University, Tehran, Iran
Keywords: graphical metric spaces, best proximity point, $\mathcal{J}$-quasi-contraction, orbitally $\mathcal{J}$-continuous,
Abstract :
The underlying aim of this paper is first to state the cyclicversion of $\mathcal{J}$-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 $\vartheta$-close elements.
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