Best Proximity Results with Applications to Nonlinear Dynamical Systems

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.