Weak compactness and the Eisenfeld-Lakshmikantham measure of nonconvexity
Isabel Marrero · Fixed Point Theory and Applications · 2012
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. Mathematics Subject Classification 2010 : Primary 47H10; Secondary 46B20, 47H08, 47H09.