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

Watchareepan Atiponrat, Anchalee Khemphet, Wipawinee Chaiwino, Teeranush Suebcharoen and Phakdi Charoensawan ()
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Watchareepan Atiponrat: Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
Anchalee Khemphet: Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
Wipawinee Chaiwino: Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
Teeranush Suebcharoen: Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
Phakdi Charoensawan: Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand

Mathematics, 2024, vol. 12, issue 2, 1-21

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.

Keywords: dominating proximal; generalized Geraghty; best proximity point; common proximity point; graph; climate change (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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