## On asymptotically nonexpansive mappings in hyperconvex metric spaces.(English)Zbl 1043.47040

The author considers the fixed point property for nonexpansive mappings in bounded hyperconvex metric spaces. He extends his results to asymptotically nonexpansive mappings. The main result states that the approximate fixed property holds in this case. The proof is based on the use, for the first time, of the ultrapower of a metric space.

### MSC:

 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47H10 Fixed-point theorems
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