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Best Proximity Results with Applications to Nonlinear Dynamical Systems

Author

Listed:
  • Hamed H Al-Sulami

    (Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Nawab Hussain

    (Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Jamshaid Ahmad

    (Department of Mathematics, University of Jeddah, P.O.Box 80327, Jeddah 21589, Saudi Arabia)

Abstract

Best proximity point theorem furnishes sufficient conditions for the existence and computation of an approximate solution ω that is optimal in the sense that the error σ ( ω , J ω ) assumes the global minimum value σ ( θ , ϑ ) . The aim of this paper is to define the notion of Suzuki α - Θ -proximal multivalued contraction and prove the existence of best proximity points ω satisfying σ ( ω , J ω ) = σ ( θ , ϑ ) , where J is assumed to be continuous or the space M is regular. We derive some best proximity results on a metric space with graphs and ordered metric spaces as consequences. We also provide a non trivial example to support our main results. As applications of our main results, we discuss some variational inequality problems and dynamical programming problems.

Suggested Citation

  • Hamed H Al-Sulami & Nawab Hussain & Jamshaid Ahmad, 2019. "Best Proximity Results with Applications to Nonlinear Dynamical Systems," Mathematics, MDPI, vol. 7(10), pages 1-20, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:900-:d:270910
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    References listed on IDEAS

    as
    1. Mohamed Jleli & Erdal Karapınar & Bessem Samet, 2013. "Best Proximity Points for Generalized -Proximal Contractive Type Mappings," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-10, May.
    2. Erdal Karapınar & Chi-Ming Chen & Chih-Te Lee, 2019. "Best Proximity Point Theorems for Two Weak Cyclic Contractions on Metric-Like Spaces," Mathematics, MDPI, vol. 7(4), pages 1-11, April.
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