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

Acta mathematica scientia,Series A ›› 2025, Vol. 45 ›› Issue (1): 256-268.

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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

Zhang Yuting, Gao Xinghui, Peng Jianying

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), the Fourteenth Five-Year Plan Mid-long Term Major Research Program of Yan'an University (2021ZCQ012), the Shaanxi Special Support Plan for High-level Talent Program (2021), the Science Research Program of Yan'an University (2023JBZR-012) and the Innovation Project of Yan'an University Graduate Education (YCX2024046)

Abstract

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

CLC Number:

O177.91

Zhang Yuting, Gao Xinghui, Peng Jianying. 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.

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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

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