Strong convergence theorems for a general system of variational inequality problems, mixed equilibrium problems and fixed points problems with applications
In this paper, we introduce a new iterative scheme for finding a common element of the set of solutions of a general system of variational inequalities, the set of solutions of a mixed equilibrium problem and the set of common fixed points of a finite family of nonexpansive mappings in a real Hilber...
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| Main Authors: | , |
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| Format: | Journal |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=77956012985&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/50708 |
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| Institution: | Chiang Mai University |
| Summary: | In this paper, we introduce a new iterative scheme for finding a common element of the set of solutions of a general system of variational inequalities, the set of solutions of a mixed equilibrium problem and the set of common fixed points of a finite family of nonexpansive mappings in a real Hilbert space. Using the demi-closedness principle for nonexpansive mapping, we prove that the iterative sequence converges strongly to a common element of the above three sets under some control conditions. Our main result extends a recent result of Ceng, Wang and Yao [L.C. Ceng, C.Y. Wang and J.C. Yao, Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities, Math. Meth. Oper. Res. 67 (2008) 375-390]. © 2010 Elsevier Ltd. |
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