Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On asymptotically nonexpansive mappings in hyperconvex metric spaces

Author: M. A. Khamsi
Journal: Proc. Amer. Math. Soc. 132 (2004), 365-373
MSC (2000): Primary 47H09, 47H10
Published electronically: August 28, 2003
MathSciNet review: 2022357
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Abstract: 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.

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Additional Information

M. A. Khamsi
Affiliation: Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, Texas 79968-0514

Keywords: Nonexpansive mappings, asymptotically nonexpansive mappings, fixed point, hyperconvex
Received by editor(s): March 12, 2002
Published electronically: August 28, 2003
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2003 American Mathematical Society