Firmly nonexpansive mappings in classes of geodesic spaces
David Ariza‐Ruiz, Laurenţiu Leuştean, Genaro López-Acedo · Transactions of the American Mathematical Society · 2014
Firmly 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 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.