An iterative method for solving proximal split feasibility problems and fixed point problems
- 79 Downloads
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.
KeywordsFixed point problems Proximal split feasibility problems Nonexpansive mappings
Mathematics Subject Classification47H09 47H10
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.
- Browder FE (1976) Nonlinear operators and nonlinear equations of evolution in Banach spaces. Proc. Symp. Pure Math. 18:78–81Google Scholar
- Cegielski A (2012) Iterative methods for fixed point problems in Hilbert spaces. Lecture notes in mathematics, vol 2057. Springer, HeidelbergGoogle Scholar
- Combettes PL, Pesquet JC (2011a) Proximal splitting methods in signal processing. In: Fixed-point algorithms for inverse problems in science and engineering. Springer, New York, pp 185–212Google Scholar