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

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Abstract
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.
Funding Information
  • Fundamental Fund 2024 Chiang Mai University
  • Chiang Mai University, Chiang Mai, Thailand
  • Faculty of Science, Chiang Mai University, Chiang Mai, Thailand

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