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

T. Domínguez Benavides and P. Lorenzo Ramírez

Abstract and Applied Analysis, 2003, vol. 2003, 1-12

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 , 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.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:172532

DOI: 10.1155/S1085337503203080

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