Weak compactness and the Eisenfeld-Lakshmikantham measure of nonconvexity

Abstract

In this article, weakly compact subsets of real Banach spaces are characterized in terms of the Cantor property for the Eisenfeld-Lakshmikantham measure of nonconvexity. This characterization is applied to prove the existence of fixed points for condensing maps, nonexpansive maps, and isometries without convexity requirements on their domain. © 2012 Marrero; licensee Springer.