# An iterative method for solving proximal split feasibility problems and fixed point problems

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## Abstract

The purpose of this research is to introduce a regularized algorithm based on the viscosity method for solving the proximal split feasibility problem and the fixed point problem in Hilbert spaces. A strong convergence result of our proposed algorithm for finding a common solution of the proximal split feasibility problem and the fixed point problem for nonexpansive mappings is established. We also apply our main result to the split feasibility problem, and the fixed point problem of nonexpansive semigroups, respectively. Finally, we give numerical examples for supporting our main result.

## Keywords

Fixed point problems Proximal split feasibility problems Nonexpansive mappings## Mathematics Subject Classification

47H09 47H10## Notes

### Acknowledgements

The authors would like to thank the referees for valuable comments and suggestions for improving this work. W. Khuangsatung would like to thank Rajamangala University of Technology Thanyaburi and S. Suantai would like to thank Chiang Mai University for the financial support.

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