The Jordan–von Neumann constants and fixed points for multivalued nonexpansive mappings

The purpose of this paper is to study the existence of fixed points for nonexpansive multivalued mappings in a particular class of Banach spaces. Furthermore, we demonstrate a relationship between the weakly convergent sequence coefficient WCS(X) and the Jordan–von Neumann constant CNJ(X) of a Banach space X. Using this fact, we prove that if CNJ(X) is less than an appropriate positive number, then every multivalued nonexpansive mapping T :E →KC(E) has a fixed point where E is a nonempty weakly compact convex subset of a Banach space X, and KC(E) is the class of all nonempty compact convex subsets of E. © 2005 Elsevier Inc. All rights reserved.