解决希尔伯特空间中 G 变不等式问题和赋有图的定点问题的正则化方法

IF 1.5 3区数学 Q1 MATHEMATICS

Journal of Inequalities and Applications Pub Date : 2024-01-30 DOI:10.1186/s13660-024-03089-2

Wongvisarut Khuangsatung, Akarate Singta, Atid Kangtunyakarn

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引用次数: 0

摘要

本文考虑并研究了具有图的实希尔伯特空间中的变分不等式问题和定点问题。本文提出了一种正则化方法，用于解决禀赋有图的希尔伯特空间框架中的G变分不等式问题和有限族G-无穷映射的普通定点问题，该方法扩展了Tiammee等人（《定点理论应用》，187，2015年）和Kangtunyakarn，A. （Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 112:437-448，2018年）的工作。在某些条件下，证明了所提方法的强收敛定理。最后，我们提供了数值示例来支持我们的主定理。数值实例表明，所提方法的速度优于近期文献中的一些现有方法。

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A regularization method for solving the G-variational inequality problem and fixed-point problems in Hilbert spaces endowed with graphs

This article considers and investigates a variational inequality problem and fixed-point problems in real Hilbert spaces endowed with graphs. A regularization method is proposed for solving a G-variational inequality problem and a common fixed-point problem of a finite family of G-nonexpansive mappings in the framework of Hilbert spaces endowed with graphs, which extends the work of Tiammee et al. (Fixed Point Theory Appl. 187, 2015) and Kangtunyakarn, A. (Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 112:437–448, 2018). Under certain conditions, a strong convergence theorem of the proposed method is proved. Finally, we provide numerical examples to support our main theorem. The numerical examples show that the speed of the proposed method is better than some recent existing methods in the literature.

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来源期刊

Journal of Inequalities and Applications 数学-数学

自引率

6.20%

发文量

136

期刊介绍： The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.