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

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.