A quadratic rate of asymptotic regularity for CAT(0)-spaces

2005/11/01 by Leustean, Laurentiu · 1 citation
#47H09 (Primary) 03F10 (Secondary) #47H10 #FOS: Mathematics #Functional Analysis (math.FA) #Logic (math.LO)

paper · doi:10.48550/arxiv.math/0511019

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'').

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• Quantitative results on a generalized viscosity approximation method

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