Strong convergence theorems for split variational inequality problems in Hilbert spaces

Wenlong Sun; Gang Lu; Yuanfeng Jin; Zufeng Peng; Wenlong Sun; Gang Lu; Yuanfeng Jin; Zufeng Peng

doi:10.3934/math.20231396

AIMS Mathematics

2023, Volume 8, Issue 11: 27291-27308. doi: 10.3934/math.20231396

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Research article

Strong convergence theorems for split variational inequality problems in Hilbert spaces

Wenlong Sun ^1,2,3,
Gang Lu ^{4
,
,},
Yuanfeng Jin ^{2
,
,},
Zufeng Peng ^{5
,
,}

1.
Department of Mathematics, School of Science, Shenyang University of Technology, Shenyang 110870, China
2.
Department of Mathematics, Yanbian University, Yanji 133001, China
3.
Liaoning Provincial Key Laboratory of Composite Metal Nanomaterials and Magnetic Technology, Shenyang University of Technology, Shenyang 110870, China
4.
Division of Foundational Teaching, Guangzhou College of Technology and Business, Guangzhou 510850, China
5.
Department of Mathematics, School of Science, Northeastern University, Shenyang 110819, China

Received: 25 June 2023 Revised: 24 August 2023 Accepted: 31 August 2023 Published: 26 September 2023
MSC : Primary 47H09, 47H10, 49J40

In this paper, we consider the variational inequality problem and the split common fixed point problem. Considering the common fixed points of an infinite family of nonexpansive mappings, instead of just the fixed point of one nonexpansive mapping, we generalize the results of Tian and Jiang. By removing a projection operator, we improve the efficiency of our algorithm. Finally, we propose a very simple modification to the extragradient method, which gives our algorithm strong convergence properties. We also provide some numerical examples to illustrate our main results.
- split common fixed point,
- variational inequality problem,
- nonexpansive mapping
Citation: Wenlong Sun, Gang Lu, Yuanfeng Jin, Zufeng Peng. Strong convergence theorems for split variational inequality problems in Hilbert spaces[J]. AIMS Mathematics, 2023, 8(11): 27291-27308. doi: 10.3934/math.20231396

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Abstract

In this paper, we consider the variational inequality problem and the split common fixed point problem. Considering the common fixed points of an infinite family of nonexpansive mappings, instead of just the fixed point of one nonexpansive mapping, we generalize the results of Tian and Jiang. By removing a projection operator, we improve the efficiency of our algorithm. Finally, we propose a very simple modification to the extragradient method, which gives our algorithm strong convergence properties. We also provide some numerical examples to illustrate our main results.

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