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Zbl 1103.03057
Leustean, L.
A quadratic rate of asymptotic regularity for CAT(0)-spaces. (English)
[J] J. Math. Anal. Appl. 325, No. 1, 386-399 (2007). ISSN 0022-247X

Summary: We obtain a quadratic bound on the rate of asymptotic regularity for the Krasnosels\-kij-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 2000:: *03F07 Structure of proofs
47H09 Mappings defined by "shrinking" properties
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: proof mining; metric fixed point theory; nonexpansive functions; asymptotic regularity; CAT(0)-spaces; uniformly convex hyperbolic spaces

Cited in: Zbl 1217.47117

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