Fixed points of asymptotically regular nonexpansive mappings on nonconvex sets

Wieslawa Kaczor

Abstract and Applied Analysis, 2003, vol. 2003, 1-9

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 { C i : 1 ≤ i ≤ n   } of X , and each C i 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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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:724391

DOI: 10.1155/S1085337503205054

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