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

  • Wongvisarut Khuangsatung
  • Pachara Jailoka
  • Suthep SuantaiEmail author


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.


Fixed point problems Proximal split feasibility problems Nonexpansive mappings 

Mathematics Subject Classification

47H09 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.


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Computer Science, Faculty of Science and TechnologyRajamangala University of Technology Thanyaburi (RMUTT)ThanyaburiThailand
  2. 2.Data Science Research Center, Department of Mathematics, Faculty of ScienceChiang Mai UniversityChiang MaiThailand

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