Fixed points of asymptotically regular nonexpansive mappings on nonconvex sets

Wiesława Kaczor

Abstract and Applied Analysis, 2003, vol. 2003, issue 2, 83-91

Abstract: It is shown that if X is a Banach space and C is a union of finitely many nonempty, pairwise disjoint, closed, and connected subsets {Ci : 1 ≤ i ≤ n } of X, and each Ci has the fixed‐point property (FPP) for asymptotically regular nonexpansive mappings, then any asymptotically regular nonexpansive self‐mapping of C has a fixed point. We also generalize the Goebel‐Schöneberg theorem to some Banach spaces with Opial′s property.

Date: 2003
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https://doi.org/10.1155/S1085337503205054

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2003:y:2003:i:2:p:83-91

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