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 

Pages (fromto)  790805 
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