Optimization Results for Cyclic Proximal Non-Self Mappings and Application to a System of Differential Equations

Abstract

In this paper, we investigate best proximity point results for two non-self proximal mappings $\mathcal{K}:\mathcal{M}\longrightarrow\mathcal{N}$ and $\mathcal{X}:\mathcal{N}\to\mathcal{M}$ using the weak P-property and proximal cyclic contraction. We present an example to illustrate the main result and provide an application of our main theorem to a system of differential equations.