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On quantitative versions of theorems due to F.E. Browder and R. Wittmann by Ulrich Kohlenbach is a Mathematics article available to read on EtoBox.

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This paper is another case study in the program of logically analyzing proofs to extract new (typically effective) information ('proof mining'). We extract explicit uniform rates of metastability (in the sense of T. Tao) from two ineffective proofs of a classical theorem of F.E. Browder on the convergence of approximants to fixed points of nonexpansive mappings as well as from a proof of a theorem of R. Wittmann which can be viewed as a nonlinear extension of the mean ergodic theorem. The first rate is extracted from Browder's original proof that is based on an application of weak sequential compactness (in addition to a projection argument). Wittmann's proof follows a similar line of reasoning and we adapt our analysis of Browder's proof to get a quantitative version of Wittmann's theorem as well. In both cases one also obtains totally elementary proofs (even for the strengthened quantitative forms) of these theorems that neither use weak compactness nor the existence of projections anymore. In this way, the present article also discusses general features of extracting effective information from proofs based on weak compactness. We then extract another rate of metastability (of si

Who reads On quantitative versions of theorems due to F.E. Browder and R. Wittmann?

Author

Ulrich Kohlenbach

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0001-8708)

Published

2011

Language

EN

Field

Mathematics (Physical Sciences)