Common Best Proximity Point Theorems for Generalized Dominating with Graphs and Applications in Differential Equations

In this paper, we initiate a concept of graph-proximal functions. Furthermore, we give a notion of being generalized Geraghty dominating for a pair of mappings. This permits us to establish the existence of and unique results for a common best proximity point of complete metric space. Additionally,...

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Bibliographic Details
Main Authors: Watchareepan Atiponrat, Anchalee Khemphet, Wipawinee Chaiwino, Teeranush Suebcharoen, Phakdi Charoensawan
Format: Article
Language:English
Published: MDPI AG 2024-01-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/12/2/306
Description
Summary:In this paper, we initiate a concept of graph-proximal functions. Furthermore, we give a notion of being generalized Geraghty dominating for a pair of mappings. This permits us to establish the existence of and unique results for a common best proximity point of complete metric space. Additionally, we give a concrete example and corollaries related to the main theorem. In particular, we apply our main results to the case of metric spaces equipped with a reflexive binary relation. Finally, we demonstrate the existence of a solution to boundary value problems of particular second-order differential equations.
ISSN:2227-7390