A new metastable convergence criterion and an application in the theory of uniformly convex Banach spaces

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Abstract

We study a convergence criterion which generalises the notion of being monotonically decreasing, and introduce a quantitative version of this criterion, a so called metastable rate of asymptotic decreasingness. We then present a concrete application in the fixed point theory of uniformly convex Banach spaces, in which we carry out a quantitative analysis of a convergence proof of Kirk and Sims. More precisely, we produce a rate of metastability (in the sense of Tao) for the Picard iterates of mappings which satisfy a variant of the convergence criterion, and whose fixed point set has nonempty interior.
Original languageEnglish
Pages (from-to)790-805
Number of pages16
JournalJournal of Mathematical Analysis and Applications
Volume478
Issue number2
Early online date31 May 2019
DOIs
Publication statusPublished - 15 Oct 2019

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