Measures of noncompactness and some applications

Abstract

This paper contains a survey of the most important basic properties of certain measures of noncompactness on bounded sets of complete metric spaces and Banach spaces, and of the Hausdorff measure of noncompactness of operators between Banach spaces. We also demonstrate how the theory of measures of noncompactness can be applied in fixed point theory, the theory of differential and integral equations, and the characterizations of classes of compact operators between certain Banach spaces.