Hilbert 空间中不动点问题, 变分不等式系统和分裂均衡问题迭代算法的强收敛定理

数学物理学报 ›› 2023, Vol. 43 ›› Issue (6): 1880-1896.

Hilbert 空间中不动点问题, 变分不等式系统和分裂均衡问题迭代算法的强收敛定理

潘灵荣^1,^*(),王元恒²

¹浙江开放大学温岭学院浙江温岭 317500
²浙江师范大学数学与计算机科学学院浙江金华 321004

收稿日期:2022-08-26 修回日期:2023-05-17 出版日期:2023-12-26 发布日期:2023-11-16
通讯作者: *潘灵荣，E-mail: 2671825414@qq.com
基金资助:
国家自然科学基金(12171435);浙江省教育厅科研项目(Y202146280)

The Strong Convergence Theorem of Iterative Algorithms for the Fixed Point Problem, a System of Variational Inequalities, and a Split Equilibrium Problem in Hilbert Spaces

Pan Lingrong^1,^*(),Wang Yuanheng²

¹Wenling Institute, Zhejiang Open University, Zhejiang Wenling 317500
²College of Mathematics and Computer Science, Zhejiang Normal University, Zhejiang Jinhua 321004

Received:2022-08-26 Revised:2023-05-17 Online:2023-12-26 Published:2023-11-16
Supported by:
NSFC(12171435);Scientific Research Fund of Zhejiang Province Education Depertment(Y202146280)

摘要/Abstract

摘要：

在 Hilbert 空间中, 考虑渐近非扩张映像的不动点问题, 变分不等式系统和分裂均衡问题的一个公共解. 在适当的参数限制条件下, 证明了所构造的修正粘性迭代序列强收敛到以上三类问题的一个公共元, 所得结论改进和推广了一些最近文献的相关结果.

关键词: 渐近非扩张映像, 变分不等式系统, 分裂均衡问题, 不动点问题

Abstract:

In this paper, we consider a common solution of three problems in real Hilbert spaces including the fixed points problem for asymptotically nonexpansive mapping, a system of variational inequalities and the split equilibrium problem. Under some suitable conditions imposed on the sequence of parameters, we prove that the sequence generated by the modified viscosity approximation method converges strongly to a common element of the solution set of these three kinds of problems. The results obtained in this article extend and improve the corresponding results of the relevant literature.

Key words: Asymptotically nonexpansive mapping, System of variational inequalities, Split equilibrium problem, Fixed point problem

中图分类号:

O177.91

潘灵荣, 王元恒. Hilbert 空间中不动点问题, 变分不等式系统和分裂均衡问题迭代算法的强收敛定理[J]. 数学物理学报, 2023, 43(6): 1880-1896.

Pan Lingrong, Wang Yuanheng. The Strong Convergence Theorem of Iterative Algorithms for the Fixed Point Problem, a System of Variational Inequalities, and a Split Equilibrium Problem in Hilbert Spaces[J]. Acta mathematica scientia,Series A, 2023, 43(6): 1880-1896.

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