Fixed point theorems for multivalued nonexpansive mappings without uniform convexity
T. Domínguez Benavides, P. Lorenzo Ramírez · RePEc: Research Papers in Economics · 2003
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 , K C ( C ) the family of all compact convex subsets of C , and T a nonexpansive mapping from C into K C ( 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.