An application of a measure of noncompactness in the study of asymptotic stability

Abstract

Using the technique of fixed-point theorem of Darbo type associated with measures of noncompactness, we obtain an existence result for some functional-integral equation. Moreover, the choice of suitable measure of noncompactness allows us to characterize solutions of the considered equation in terms of asymptotic stability. The method applied here also creates a generalization of the classical Banach fixed- point principle.