Best proximity point results of operator type condensing mappings via measure of noncompactness and application to an infinite system of differential equations in $c_0$ and ${\mathrm{\ell }}_1$

We propose a new class of cyclic (noncyclic) operator type condensing mappings and establish conditions that guarantee the existence of best proximity points (pairs) using measure of noncompactness. The results obtained are further applied to investigate the optimum solution of an infinite system of differential equations in $c_0$ and ${\mathrm{\ell }}_1$.