Best Proximity Results with Applications to Nonlinear Dynamical Systems - Hamed H Al-Sulami; Nawab Hussain; Jamshaid Ahmad (Mathematics, 2019)
Best proximity point theorem furnishes sufficient conditions for the existence and computation of an approximate solution <semantics> ω </semantics> that is optimal in the sense that the error <semantics> σ ( ω , J ω ) </semantics> assumes the global minimum value <semantics> σ ( θ , ϑ ) </semantics> . The aim of this paper is to define the notion of Suzuki <semantics> α </semantics> - <semantics> Θ </semantics> -proximal multivalued contraction and prove the existence of best proximity points <semantics> ω </semantics> satisfying <semantics> σ ( ω , J ω ) = σ ( θ , ϑ ) , </semantics> where <semantics> J </semantics> is assumed to be continuous or the space <semantics> M </semantics> 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.