Graphical cyclic $\mathcal{J}$-integral Banach type mappings and the existence of their best proximity points

Subject Areas : Operator theory

K.  Fallahi ¹ (Department of Mathematics, Payame Noor University, Tehran, Iran)
S.  Jalali ² (Department of Mathematics, Payame Noor University, Tehran, Iran)

Received: 2023-12-16 Accepted : 2024-01-24 Published : 2024-03-07

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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