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A quadratic rate of asymptotic regularity for CAT(0)-spaces. (English) Zbl 1103.03057
Summary: We obtain a quadratic bound on the rate of asymptotic regularity for the Krasnoselskij-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”).

MSC:
03F07 Structure of proofs
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
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