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Bounds for a nonlinear ergodic theorem for Banach spaces

Part of: Proof theory and constructive mathematics Nonlinear operators and their properties

Published online by Cambridge University Press:  18 February 2022

ANTON FREUND Open the ORCID record for ANTON FREUND [Opens in a new window]  and
ULRICH KOHLENBACH Open the ORCID record for ULRICH KOHLENBACH [Opens in a new window]
ANTON FREUND*
Affiliation:
Department of Mathematics, Technical University of Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, Germany (e-mail: kohlenbach@mathematik.tu-darmstadt.de)
ULRICH KOHLENBACH
Affiliation:
Department of Mathematics, Technical University of Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, Germany (e-mail: kohlenbach@mathematik.tu-darmstadt.de)
*
e-mail: freund@mathematik.tu-darmstadt.de
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Abstract

We extract quantitative information (specifically, a rate of metastability in the sense of Terence Tao) from a proof due to Kazuo Kobayasi and Isao Miyadera, which shows strong convergence for Cesàro means of non-expansive maps on Banach spaces.

Keywords

nonlinear ergodic theoremBanach spacequantitative analysisproof miningmetastability

MSC classification

Primary: 47H10: Fixed-point theorems
Secondary: 03F10: Functionals in proof theory
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 43 , Issue 5 , May 2023 , pp. 1570 - 1593
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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