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, issue 6, 375-386

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.

Date: 2003
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https://doi.org/10.1155/S1085337503203080

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2003:y:2003:i:6:p:375-386

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