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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 18
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Research Article

Strong convergence of two regularized relaxed extragradient schemes for solving the split feasibility and fixed point problem with multiple output sets

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Pages 5132-5156 | Received 20 Sep 2022, Accepted 31 Dec 2022, Published online: 12 Jan 2023
 

Abstract

We study the split feasibility and fixed point problem with multiple output sets in real Hilbert spaces. Using Tikhonov's regularization and viscosity approximation techniques, we propose two relaxed extragradient algorithms for finding approximate solutions to this problem and prove that the sequences they generate converge strongly. Finally, we give some consequences and an application of our results, and also present numerical examples to validate the efficiency of our algorithms.

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Acknowledgments

All the authors thank two anonymous referees for their pertinent comments and useful suggestions.

Disclosure statement

The authors declare that they have no conflict of interest.

Additional information

Funding

Simeon Reich was partially supported by the Israel Science Foundation (Grant No. 820/17), by the Fund for the Promotion of Research at the Technion and by the Technion General Research Fund.

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