Ariza Ruiz, DavidLeustean, LaurentiuLópez Acedo, Genaro2016-06-222016-06-222014Ariza Ruiz, D., Leustean, L. y López Acedo, G. (2014). Firmly nonexpansive mappings in classes of geodesic spaces. Transactions of the American Mathematical Society, 366 (8), 4299-4322.0002-99471088-6850http://hdl.handle.net/11441/42604Firmly nonexpansive mappings play an important role in metric fixed point theory and optimization due to their correspondence with maximal monotone operators. In this paper we do a thorough study of fixed point theory and the asymptotic behaviour of Picard iterates of these mappings in different classes of geodesic spaces, such as (uniformly convex) W-hyperbolic spaces, Busemann spaces and CAT(0) spaces. Furthermore, we apply methods of proof mining to obtain effective rates of asymptotic regularity for the Picard iterations.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/firmly nonexpansive mappingsgeodesic spacesuniform convexityPicard iteratesasymptotic regularity∆-convergenceproof miningeffective boundsminimization problemsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1090/S0002-9947-2014-05968-0