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Strong convergence of a general viscosity explicit rule for the sum of two monotone operators in Hilbert spaces |
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| Authors: | Prasit Cholamjiak Suthep Suantai Pongsakorn Sunthrayuth |
| Affiliation: | School of Science, University of Phayao, Phayao 56000, Thailand,Department of Mathematics, Faculty of Science, Chiang Mai University, Chi- ang Mai 50200, Thailand and Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Pathumthani, Thailand |
| Abstract: | In this paper, we study a general viscosity explicit rule for approximating the solutions of the variational inclusion problem for the sum of two monotone operators. We then prove its strong convergence under some new conditions on the parameters in the framework of Hilbert spaces. As applications, we apply our main result to the split feasibility problem and the LASSO problem. We also give some numerical examples to support our main result. The results presented in this paper extend and improve the corresponding results in the literature. |
| Keywords: | Monotone operator Hilbert space strong convergence iterative method. |
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