A quadratic rate of asymptotic regularity for CAT(0)-spaces
Functional Analysis
2007-05-23 v1 Logic
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'').
Keywords
Cite
@article{arxiv.math/0511019,
title = {A quadratic rate of asymptotic regularity for CAT(0)-spaces},
author = {Laurentiu Leustean},
journal= {arXiv preprint arXiv:math/0511019},
year = {2007}
}
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17 pages