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Some Results on Multivalued Proximal Contractions with Application to Integral Equation

Author

Listed:
  • Muhammad Zahid

    (Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan)

  • Fahim Ud Din

    (Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan)

  • Mudasir Younis

    (Department of Mathematics, Faculty of Sciences, Sakarya University, Sakarya 54050, Turkey)

  • Haroon Ahmad

    (Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan)

  • Mahpeyker Öztürk

    (Department of Mathematics, Faculty of Sciences, Sakarya University, Sakarya 54050, Turkey)

Abstract

In this manuscript, for the purpose of investigating the coincidence best proximity point, best proximity point, and fixed point results via alternating distance ϕ , we discuss some multivalued ( ϕ − F τ ) C P and ( ϕ − F τ ) B P − proximal contractions in the context of rectangular metric spaces. To ascertain the coincidence best proximity point, best proximity point, and the fixed point for single-valued mappings, we reduce these findings using ( F τ ) C P and ( F τ ) B P − proximal contractions. To make our work more understandable, examples of both single- and multivalued mappings are provided. These examples support our core findings, which rely on coincidence points, as well as the corollaries that address fixed point conclusions. In the final phase of our study, we use the obtained results to verify that a solution to a Fredholm integral equation exists. This application highlights the theoretical framework we built throughout our study.

Suggested Citation

  • Muhammad Zahid & Fahim Ud Din & Mudasir Younis & Haroon Ahmad & Mahpeyker Öztürk, 2024. "Some Results on Multivalued Proximal Contractions with Application to Integral Equation," Mathematics, MDPI, vol. 12(22), pages 1-21, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3488-:d:1516443
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    References listed on IDEAS

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    1. N. Shahzad & S. Sadiq Basha & R. Jeyaraj, 2011. "Common Best Proximity Points: Global Optimal Solutions," Journal of Optimization Theory and Applications, Springer, vol. 148(1), pages 69-78, January.
    2. Naeem Saleem & Haroon Ahmad & Hassen Aydi & Yaé Ulrich Gaba & Efthymios G. Tsionas, 2021. "On Some Coincidence Best Proximity Point Results," Journal of Mathematics, Hindawi, vol. 2021, pages 1-19, December.
    3. A. Abkar & M. Gabeleh, 2011. "Best Proximity Points for Cyclic Mappings in Ordered Metric Spaces," Journal of Optimization Theory and Applications, Springer, vol. 150(1), pages 188-193, July.
    4. Haroon Ahmad & Mudasir Younis & Mehmet Emir Koksal & Durdana Lateef & Palanivel M., 2024. "Nonunique Fixed-Point Results in a General Setting with an Application," Journal of Mathematics, Hindawi, vol. 2024, pages 1-13, July.
    5. S. Sadiq Basha, 2011. "Best proximity points: global optimal approximate solutions," Journal of Global Optimization, Springer, vol. 49(1), pages 15-21, January.
    6. A. Abkar & M. Gabeleh, 2011. "Best Proximity Points for Cyclic Mappings in Ordered Metric Spaces," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 418-424, November.
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