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Quantitative inconsistent feasibility for averaged mappings

Abstract

Bauschke and Moursi have recently obtained results that implicitly contain the fact that the composition of finitely many averaged mappings on a Hilbert space that have approximate fixed points also has approximate fixed points and thus is asymptotically regular. Using techniques of proof mining, we analyze their arguments to obtain effective uniform rates of asymptotic regularity.

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Acknowledgements

I would like to thank Ulrich Kohlenbach for pointing me to the paper [6] and for suggesting an improvement of Proposition 2.7. This work has been supported by the German Science Foundation (DFG Project KO 1737/6-1) and by a grant of the Romanian Ministry of Research, Innovation and Digitization, CNCS/CCCDI – UEFISCDI, Project Number PN-III-P1-1.1-PD-2019-0396, within PNCDI III.

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Correspondence to Andrei Sipoş.

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Sipoş, A. Quantitative inconsistent feasibility for averaged mappings. Optim Lett (2021). https://doi.org/10.1007/s11590-021-01812-2

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Keywords

  • Proof mining
  • Averaged mappings
  • Nonexpansive mappings
  • Resolvents
  • Rates of asymptotic regularity