希尔伯特空间中平均半闭映射的Ishikawa和混合方法的强收敛性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-03-21 DOI:10.3846/mma.2023.15843

Atsumasa Kondo

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引用次数: 0

摘要

本文综合运用石川迭代法、混合迭代法和中值迭代法，建立了逼近两个非线性映射的一个公共不动点的强收敛定理。提出了收缩投影法。非线性映射是一种一般类型，包括非扩展映射和其他类型的已知映射。不假定这两个映射是连续的或可交换的。本文的主要定理生成了包括一类“三步迭代法”在内的各种强收敛定理。并给出了该方法在变分不等式问题中的应用。

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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Strong convergence to Common fixed Points using Ishikawa and Hybrid Methods for mean-Demiclosed mappings in Hilbert Spaces

In this paper, we establish a strong convergence theorem that approximates a common fixed point of two nonlinear mappings by comprehensively using an Ishikawa iterative method, a hybrid method, and a mean-valued iterative method. The shrinking projection method is also developed. The nonlinear mappings are a general type that includes nonexpansive mappings and other classes of well-known mappings. The two mappings are not assumed to be continuous or commutative. The main theorems in this paper generate a variety of strong convergence theorems including a type of “three-step iterative method”. An application to the variational inequality problem is also given.

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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.