a Department of Mathematics, Darmstadt University of Technology, Schlossgartenstrasse 7, 64289 Darmstadt, Germany b Institute of Mathematics “Simion Stoilow” of the Romanian Academy, Calea Grivitei 21, PO Box 1-462, Bucharest, Romania
Abstract:
In this paper we obtain a quadratic bound on the rate of asymptotic regularity for the Krasnoselski-Mann iterations of nonexpansive mappings in CAT(0)-spaces, whereas previous results guarantee only exponential bounds. The method we use is to extend to the more general setting of uniformly convex hyperbolic spaces a quantitative version of a strengthening of Groetsch's theorem obtained by Kohlenbach using methods from mathematical logic (so-called “proof mining”).