An inertial method for solving split common fixed point problems
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In this paper, we introduce a new algorithm which combines the Mann iteration and the inertial method for solving split common fixed point problems. The weak convergence of the algorithm is established under standard assumptions imposed on cost operators. As a consequence, we obtain weak convergence theorems for split variational inequality problems for inverse strongly monotone operators, and split common null point problems for maximal monotone operators. Finally, for supporting the convergence of the proposed algorithms we also consider several preliminary numerical experiments on a test problem.
KeywordsSplit common fixed point problem split feasibility problem split variational inequality problem split null point problem
Mathematics Subject Classification47H10 47J25 47H45 65J15
The authors are grateful to the anonymous referee for valuable suggestions which helped to improve the manuscript. The first author was partially supported by Vietnam Institute for Advanced Study in Mathematics (VIASM). The second author was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under the project 101.01-2017.315.
- 21.Dang, Y., Sun, J., Xu, H.: Inertial accelerated algorithms for solving a split feasibility problem. J. Ind. Manag. Optim. 13, 1383–1394 (2017)Google Scholar
- 36.Polyak, B.T.: Some methods of speeding up the convergence of iterarive methods. Zh. Vychisl. Mat. Mat. Fiz. 4, 1–17 (1964)Google Scholar
- 43.Thong, D.V.: Viscosity approximation methods for solving fixed point problems and split common fixed point problems. J. Fixed Point Theory Appl. 19, 1481–1499 (2017)Google Scholar
- 44.Thong, D.V., Hieu, D.V.: An inertial subgradient extragradient method for variational inequality problems. Optimization (2017) (Revised)Google Scholar