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

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.

Keywords:

• Split feasibility and fixed point problem
• pseudocontractive mapping
• Hilbert space
• strong convergence

AMS SUBJECT CLASSIFICATION 2020:

• 47H10
• 47H09
• 47J25
• 47B02

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.