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

• Main Authors: S. Dhompongsa, T. Domínguez Benavides, A. Kaewcharoen, A. Kaewkhao, B. Panyanak
• Format: Journal
• Published: 2018
• Subjects: Mathematics
• Online Access: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=33646362519&origin=inward; http://cmuir.cmu.ac.th/jspui/handle/6653943832/61772
• Institution: Chiang Mai University

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.