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Effective results on nonlinear ergodic averages in CAT$(\unicode[STIX]{x1D705})$ spaces

Published online by Cambridge University Press:  21 July 2015

LAURENŢIU LEUŞTEAN Open the ORCID record for LAURENŢIU LEUŞTEAN [Opens in a new window]  and
ADRIANA NICOLAE
LAURENŢIU LEUŞTEAN
Affiliation:
Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, P.O. Box 010014, Bucharest, Romania Simion Stoilow Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-014700 Bucharest, Romania email Laurentiu.Leustean@imar.ro
ADRIANA NICOLAE
Affiliation:
Department of Mathematics, Babeş-Bolyai University, Kogălniceanu 1, 400084 Cluj-Napoca, Romania Simion Stoilow Institute of Mathematics of the Romanian Academy, Research group of the project PD-3-0152, P.O. Box 1-764, RO-014700 Bucharest, Romania email anicolae@math.ubbcluj.ro
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Abstract

In this paper we apply proof mining techniques to compute, in the setting of CAT$(\unicode[STIX]{x1D705})$ spaces (with $\unicode[STIX]{x1D705}>0$), effective and highly uniform rates of asymptotic regularity and metastability for a nonlinear generalization of the ergodic averages, known as the Halpern iteration. In this way, we obtain a uniform quantitative version of a nonlinear extension of the classical von Neumann mean ergodic theorem.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 8 , December 2016 , pp. 2580 - 2601
Copyright
© Cambridge University Press, 2015 

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