Strong convergence of the composition of firmly nonexpansive mappings

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-27 DOI:10.1007/s10898-024-01417-w

José Márcio Machado de Brito, João Xavier da Cruz Neto, Ítalo Dowell Lira Melo

引用次数: 0

Abstract

In this paper, we provide a necessary and sufficient condition under which the compositions of finitely many firmly nonexpansive mappings in a p-uniformly convex space converge strongly. In particular, we obtain convergence results for the method of alternating projections in CAT(\(\kappa \)) spaces, with \(\kappa \ge 0\). We also study the rate of convergence of the sequence generated by the method in cases where the firmly nonexpansive mappings satisfy an error bound, and the set of fixed points of these mappings is boundedly linearly regular.

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坚定非展开映射组成的强收敛性

在本文中，我们提供了一个必要条件和充分条件，在这个条件下，p-均匀凸空间中有限多个坚定非展开映射的组合会强收敛。特别是，我们得到了 CAT(\(\kappa \))空间中交替投影法的收敛结果，其中 \(\kappa \ge 0\).我们还研究了在坚定的非膨胀映射满足误差约束，并且这些映射的定点集合是有界线性规则的情况下，该方法所产生的序列的收敛率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.