Abstract and Applied Analysis
Volume 2003 (2003), Issue 6, Pages 375-386

Fixed-point theorems for multivalued non-expansive mappings without uniform convexity

T. Domínguez Benavides and P. Lorenzo Ramírez

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.


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.