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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