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

Abstract

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.