Best Proximity Results with Applications to Nonlinear Dynamical Systems

Hamed H Al-Sulami, Nawab Hussain and Jamshaid Ahmad
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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

Mathematics, 2019, vol. 7, issue 10, 1-20

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.

Keywords: nonlinear dynamical systems; best proximity point; ? -proximal contraction; multi-valued mappings; graphs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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