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 language | English |
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Pages (from-to) | 790-805 |
Number of pages | 16 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 478 |
Issue number | 2 |
Early online date | 31 May 2019 |
DOIs | |
Publication status | Published - 15 Oct 2019 |
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Thomas Powell
- Department of Computer Science - Senior Lecturer
- Mathematical Foundations of Computation
Person: Research & Teaching