Best Proximity Results with Applications to Nonlinear Dynamical Systems

Mathematics

Nawab Hussain¹  HamedH Al-Sulami¹  Jamshaid Ahmad² 

[1] Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia;Department of Mathematics, University of Jeddah, P.O.Box 80327, Jeddah 21589, Saudi Arabia;

关键词: nonlinear dynamical systems;    best proximity point;    α-proximal contraction;    multi-valued mappings;    graphs;   

DOI  :  10.3390/math7100900

来源: DOAJ

【 摘 要 】

Best proximity point theorem furnishes sufficient conditions for the existence and computation of an approximate solution $\omega$ that is optimal in the sense that the error $\sigma (\omega ,\mathcal{J}\omega )$ assumes the global minimum value $\sigma (\theta ,\vartheta )$ . The aim of this paper is to define the notion of Suzuki $\alpha$ - $\Theta$ -proximal multivalued contraction and prove the existence of best proximity points $\omega$ satisfying $\sigma (\omega ,\mathcal{J}\omega )=\sigma (\theta ,\vartheta ),$ where $\mathcal{J}$ is assumed to be continuous or the space $\mathcal{M}$ 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.

【 授权许可】

Unknown