Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 596952, 12 pages
doi:10.1155/2010/596952
Research Article

On Some Geometric Constants and the Fixed Point Property for Multivalued Nonexpansive Mappings

Jingxin Zhang1 and Yunan Cui2

1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
2Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China

Received 30 July 2010; Accepted 5 October 2010

Academic Editor: L. Górniewicz

Copyright © 2010 Jingxin Zhang and Yunan Cui. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We show some geometric conditions on a Banach space X concerning the Jordan-von Neumann constant, Zbăganu constant, characteristic of (separation) noncompact convexity, and the coefficient R(1, X), the weakly convergent sequence coefficient, which imply the existence of fixed points for multivalued nonexpansive mappings.