This paper provides a ﬁxed point theorem for asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces as well as new effective results on the Krasnosel’skiĭ–Mann iterations of such mappings. The latter were found using methods from logic and the paper continues a case study in the general program of extracting effective data from prima-facie ineffective proofs in the ﬁxed point theory of such mappings.
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Ulrich Kohlenbach, Laurentiu Leuştean, Asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces. J. Eur. Math. Soc. 12 (2010), no. 1, pp. 71–92DOI 10.4171/JEMS/190