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

Author

Listed:
  • Watchareepan Atiponrat

    (Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
    Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Anchalee Khemphet

    (Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
    Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Wipawinee Chaiwino

    (Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
    Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Teeranush Suebcharoen

    (Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
    Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Phakdi Charoensawan

    (Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
    Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

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.

Suggested Citation

  • Watchareepan Atiponrat & Anchalee Khemphet & Wipawinee Chaiwino & Teeranush Suebcharoen & Phakdi Charoensawan, 2024. "Common Best Proximity Point Theorems for Generalized Dominating with Graphs and Applications in Differential Equations," Mathematics, MDPI, vol. 12(2), pages 1-21, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:306-:d:1321118
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    References listed on IDEAS

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    1. S. Sadiq Basha, 2012. "Common best proximity points: global minimization of multi-objective functions," Journal of Global Optimization, Springer, vol. 54(2), pages 367-373, October.
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