On asymptotically nonexpansive mappings in hyperconvex metric spaces

Since bounded hyperconvex metric spaces have the fixed point property for nonexpansive mappings, it is natural to extend such a powerful result to asymptotically nonexpansive mappings. Our main result states that the approximate fixed point property holds in this case. The proof is based on the use,...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2004-02, Vol.132 (2), p.365-373
Main Author: Khamsi, M. A.
Format: Article
Language:English
Subjects:
Applied mathematics
Banach space
Convexity
Diagonal lemma
Exact sciences and technology
Fixed point property
Mathematical analysis
Mathematics
Operator theory
Sciences and techniques of general use
Ultrapowers
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Summary:Since bounded hyperconvex metric spaces have the fixed point property for nonexpansive mappings, it is natural to extend such a powerful result to asymptotically nonexpansive mappings. Our main result states that the approximate fixed point property holds in this case. The proof is based on the use, for the first time, of the ultrapower of a metric space.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-03-07172-7