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

DOI:
https://doi.org/10.1090/S0002-9939-03-07172-7

Published electronically:
August 28, 2003

MathSciNet review:
2022357

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Abstract | References | Similar Articles | Additional Information

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

Email:
mohamed@math.utep.edu

DOI:
https://doi.org/10.1090/S0002-9939-03-07172-7

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