Journal of the European Mathematical Society
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Published online: 2009-12-23
Asymptotically nonexpansive mappings in uniformly convex hyperbolic spacesUlrich Kohlenbach and Laurentiu Leuştean (1) Technische Hochschule Darmstadt, Germany
(2) Technische Hochschule Darmstadt, Germany
This paper provides a ﬁxed point theorem for asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces as well as new effective results on the Krasnosel’skiĭ–Mann iterations of such mappings. The latter were found using methods from logic and the paper continues a case study in the general program of extracting effective data from prima-facie ineffective proofs in the ﬁxed point theory of such mappings.
Keywords: Proof mining, functionals of finite type, metric fixed point theory, asymptotically nonexpansive mappings, uniformly convex hyperbolic spaces, CAT(0)-spaces, Krasnosel’skiĭ–Mann iterations
Kohlenbach Ulrich, Leuştean Laurentiu: Asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces. J. Eur. Math. Soc. 12 (2010), 71-92. doi: 10.4171/JEMS/190