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On asymptotically nonexpansive mappings in hyperconvex metric spaces |
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| Authors: | M. A. Khamsi |
| Affiliation: | Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, Texas 79968-0514 |
| 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. |
| Keywords: | Nonexpansive mappings asymptotically nonexpansive mappings fixed point hyperconvex |
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