Strong convergence of perturbed Mann iteration for systems of variational inequality problems over the set of common fixed points of a finite family of demicontractive mappings in Banach spaces

Journal of Nonlinear Sciences and Applications Pub Date : 2024-02-14 DOI:10.22436/jnsa.017.01.04

T. Sow

引用次数: 0

Abstract

In this paper, we propose an iterative algorithm, which is based on the Mann iterative method for solving simultaneously common ﬁxed point problem with a ﬁnite family of demicontractive mappings and systems of variational inequalities involving an inﬁnite family of strongly accretive operators. Under suitable assumptions, we prove the strong convergence of this algorithm in Banach spaces. Application to systems of constrained convex minimization problem is provided to support our main results. The results of this paper improve and extend results of [M. Eslamian, C. R. Math. Acad. Sci. Paris, 355 (2017), 1168–1177], and of many others.

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巴拿赫空间中有限去收缩映射族共同定点集合上的变分不等式问题系统的扰动曼迭代的强收敛性

在本文中，我们提出了一种基于曼迭代法的迭代算法，用于同时求解具有有限族去收缩映射和涉及有限族强增量算子的变分不等式系统的共同定点问题。在适当的假设条件下，我们证明了该算法在巴拿赫空间中的强收敛性。为了支持我们的主要结果，我们还提供了对受约束凸最小化问题系统的应用。本文的结果改进并扩展了[M. Eslamian, C. R. Math. Acad. Sci. Paris, 355 (2017), 1168-1177]以及许多其他论文的结果。

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

Journal of Nonlinear Sciences and Applications MATHEMATICS, APPLIED-MATHEMATICS

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期刊介绍： The Journal of Nonlinear Science and Applications (JNSA) (print: ISSN 2008-1898 online: ISSN 2008-1901) is an international journal which provides very fast publication of original research papers in the fields of nonlinear analysis. Journal of Nonlinear Science and Applications is a journal that aims to unite and stimulate mathematical research community. It publishes original research papers and survey articles on all areas of nonlinear analysis and theoretical applied nonlinear analysis. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics. Manuscripts are invited from academicians, research students, and scientists for publication consideration. Papers are accepted for editorial consideration through online submission with the understanding that they have not been published, submitted or accepted for publication elsewhere.