Abstract and Applied Analysis
Volume 2003 (2003), Issue 6, Pages 375-386
doi:10.1155/S1085337503203080
Fixed-point theorems for multivalued non-expansive mappings without uniform convexity
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Sevilla 41080, Spain
Received 13 September 2001
Copyright © 2003 T. Domínguez Benavides and P. Lorenzo Ramírez. 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
Let X be a Banach space whose characteristic of noncompact convexity
is less than 1 and satisfies the nonstrict Opial condition. Let C be a bounded closed convex subset of X, KC(C) the family of all
compact convex subsets of C, and T a nonexpansive mapping from C into KC(C). We prove that T has a fixed point. The nonstrict Opial condition can be removed if, in addition, T is a 1-χ-contractive mapping.