Journal of the European Mathematical Society


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Volume 12, Issue 1, 2010, pp. 71–92
DOI: 10.4171/JEMS/190

Asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces

Ulrich Kohlenbach[1] and Laurentiu Leuştean[2]

(1) Fachbereich Mathematik, Technische Hochschule Darmstadt, Schlossgartenstrasse 7, D-64289, DARMSTADT, GERMANY
(2) Fachbereich Mathematik, Technische Hochschule Darmstadt, Schlossgartenstrasse 7, D-64289, 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 U, Leuştean L. Asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces. J. Eur. Math. Soc. 12 (2010), 71-92. doi: 10.4171/JEMS/190