On asymptotically nonexpansive mappings in hyperconvex metric spaces
Mohamed A. Khamsi · Proceedings of the American Mathematical Society · 2003
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.