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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:320

Article

Dhompongsa, S. ; Dominguez Benavides, T. ; Kaewcharoen, A. ; Kaewkhao, A. ; Panyanak, B.

关键词: multivalued nonexpansive mapping;    weakly convergent sequence coefficient;    Jordan-von Neumann constant;    normal structure;    regular asymptotically uniform sequence;   

DOI  :  10.1016/j.jmaa.2005.07.063

来源: Elsevier

【 摘 要 】

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 C-NJ (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. (C) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

Free