Global optimal solutions of a system of differential equations via measure of noncompactness

Abstract

We establish the existence of best proximity points (pairs) for
a new class of cyclic (noncyclic) condensing operators by using the concept of measure of noncompactness.
Our conclusions extend and improve the main results of [Indagationes Math. 29 (2018), 895-906].
By applying our results, we prove a coupled best proximity point theorem and investigate the existence of a solution
for a system of differential equations.