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

T. Domínguez Benavides and P. Lorenzo Ramírez

 Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Sevilla 41080, Spain
Received 13 September 2001

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.