A new approximation method for finding common fixed points of families of demicontractive operators and applications
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In this paper, we introduce a new strongly convergent algorithm for solving common fixed point problems in Hilbert spaces for a finite (infinite) family of demicontractive operators. As a consequence, we obtain strong convergence theorems for split common fixed point problems for a finite family of demicontractive operators, split variational inequality problems for inverse strongly monotone operators and split common null point problems for maximal monotone operators. Finally, the performance of the proposed algorithm is also illustrated by several preliminary numerical experiments.
KeywordsFixed point problem split common fixed point problem split feasibility problem split variational inequality problem split null point problem
Mathematics Subject Classification47H10 47J25 47H45 65J15
The authors would like to thank the referees for their valuable comments and suggestions which helped us very much in improving and presenting the original version of this paper. The authors would like to thank Professor Pham Ky Anh for drawing our attention to the subject and for many useful discussions.
- 22.Hieu, D.V.: An explicit parallel algorithm for variational inequalities. Bull. Malays. Math. Soc. (2017). https://doi.org/10.1007/s40840-017-0474-z
- 31.Reich, S.: Constructive Techniques for Accretive and Monotone Operators. Applied Nonlinear Analysis, pp. 335–345. Academic Press, New York (1979)Google Scholar
- 37.Thong, D.V., Hieu, D.V.: Weak and strong convergence theorems for variational inequality problems. Numer. Algorithms (2017). https://doi.org/10.1007/s11075-017-0412-z
- 38.Thong, D.V., Hieu, D.V.: Modified subgradient extragradient method for inequality variational problems. Numer. Algorithms (2017). https://doi.org/10.1007/s11075-017-0452-4
- 40.Thong D.V., Hieu, D.V.: Inertial extragradient algorithms for strongly pseudomonotone variational inequalities. J. Comput. Appl. Math. (accepted) Google Scholar