Abstract
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, J omega) assumes the global minimum value sigma(theta, theta). 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, J omega) = sigma(theta, theta), 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.