2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157361This paper provides a fixed point theorem for asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces as well as new effective results on the Krasnoselski-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.to appear in Journal of the European Mathematical Society; minor revisionFunctional AnalysisLogic47H10, 47H09, 03F10text