分裂可行性问题解集和有限族拟非扩张算子公共不动点集的公共元的迭代算法

分裂可行性问题解集和有限族拟非扩张算子公共不动点集的公共元的迭代算法

Iterative Algorithms of Common Elements for the Set of Solutions of Split Feasibility Problem and the Set of Common Fixed Points of a Finite Family of Quasi-Nonexpansive Operators

摘要/Abstract

图/表 3

参考文献 13

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数学物理学报 ›› 2025, Vol. 45 ›› Issue (1): 256-268.

张玉婷(),高兴慧^*(),彭剑英

延安大学数学与计算机科学学院陕西延安 716000

收稿日期:2024-04-12 修回日期:2024-08-12 出版日期:2025-02-26 发布日期:2025-01-08
通讯作者: * 高兴慧,E-mail:yadxgaoxinghui@163.com
作者简介:张玉婷, E-mail:zyt910945332@163.com
基金资助:
国家自然科学基金(61866038);延安大学 “十四五” 中长期重大科研项目(2021ZCQ012);陕西省特支计划人才项目(2021);延安大学科研计划项目(2023JBZR-012);延安大学研究生教育创新计划项目(YCX2024046)

Yuting Zhang(),Xinghui Gao^*(),Jianying Peng

College of Mathematics and Computer Science, Yan'an University, Shaanxi Yan'an 716000

Received:2024-04-12 Revised:2024-08-12 Online:2025-02-26 Published:2025-01-08
Supported by:
NSFC(61866038);Fourteenth Five-Year Plan Mid-long Term Major Research Program of Yan'an University(2021ZCQ012);Shaanxi Special Support Plan for High-level Talent Program(2021);Science Research Program of Yan'an University(2023JBZR-012);Innovation Project of Yan'an University Graduate Education(YCX2024046)

摘要：

在 Hilbert 空间中, 构造了寻找分裂可行性问题与有限族拟非扩张算子公共不动点问题之公共解的一种新算法. 在适当的条件下, 利用映射的次闭性和投影算子与共轭算子的性质证明了由该算法生成的迭代序列强收敛到分裂可行性问题和不动点问题的公共解, 并给出具体的数值实验验证算法的有效性. 所得结果改进和推广了一些最新文献的相关结果.

关键词: 分裂可行性问题, 不动点问题, 有限族拟非扩张算子

Abstract:

In real Hilbert spaces, we construct a new algorithm to find a common solution of the split feasibility problem and the fixed points problem involving a finite family of quasi-nonexpansive mappings. Under appropriate conditions, it is proved that the iteration sequence by the algorithm strongly converges to a common solution of the split feasibility problem and the fixed points problem by using the demi-closed principle and properties of projection operators and conjugate operators. The effectiveness of the algorithm is verified by numerical experiments. The results of this paper improve and extend recent some relative results.

Key words: split feasibility problem, fixed points problem, a finite family of quasi-nonexpansive mappings

中图分类号:

O177.91

张玉婷, 高兴慧, 彭剑英. 分裂可行性问题解集和有限族拟非扩张算子公共不动点集的公共元的迭代算法[J]. 数学物理学报, 2025, 45(1): 256-268.

Yuting Zhang, Xinghui Gao, Jianying Peng. Iterative Algorithms of Common Elements for the Set of Solutions of Split Feasibility Problem and the Set of Common Fixed Points of a Finite Family of Quasi-Nonexpansive Operators[J]. Acta mathematica scientia,Series A, 2025, 45(1): 256-268.

表 1

图1

当 $\parallel q_n-q^*\parallel\leq10^{-3}$ 时Alg1和Alg2的数值结果"

图1

表 2

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