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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:478

Article

Powell, Thomas¹ 

[1] Tech Univ Darmstadt, Dept Math, Schlossgartenstr 7, D-64289 Darmstadt, Germany

关键词: Proof mining;    Metastability;    Fixed points;    Asymptotically nonexpansive mappings;    Uniformly convex Banach spaces;   

DOI  :  10.1016/j.jmaa.2019.05.055

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free