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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th-cmuir.6653943832-61842014-08-30T03:23:56Z Strong convergence theorems for a general system of variational inequality problems, mixed equilibrium problems and fixed points problems with applications Imnang S. Suantai S. 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. 2014-08-30T03:23:56Z 2014-08-30T03:23:56Z 2010 Article 8957177 10.1016/j.mcm.2010.06.037 MCMOE http://www.scopus.com/inward/record.url?eid=2-s2.0-77956012985&partnerID=40&md5=a9cd141e9babb4e52f087165013b9c8f http://cmuir.cmu.ac.th/handle/6653943832/6184 English |
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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. |
| format |
Article |
| author |
Imnang S. Suantai S. |
| spellingShingle |
Imnang S. Suantai S. Strong convergence theorems for a general system of variational inequality problems, mixed equilibrium problems and fixed points problems with applications |
| author_facet |
Imnang S. Suantai S. |
| author_sort |
Imnang S. |
| title |
Strong convergence theorems for a general system of variational inequality problems, mixed equilibrium problems and fixed points problems with applications |
| title_short |
Strong convergence theorems for a general system of variational inequality problems, mixed equilibrium problems and fixed points problems with applications |
| title_full |
Strong convergence theorems for a general system of variational inequality problems, mixed equilibrium problems and fixed points problems with applications |
| title_fullStr |
Strong convergence theorems for a general system of variational inequality problems, mixed equilibrium problems and fixed points problems with applications |
| title_full_unstemmed |
Strong convergence theorems for a general system of variational inequality problems, mixed equilibrium problems and fixed points problems with applications |
| title_sort |
strong convergence theorems for a general system of variational inequality problems, mixed equilibrium problems and fixed points problems with applications |
| publishDate |
2014 |
| url |
http://www.scopus.com/inward/record.url?eid=2-s2.0-77956012985&partnerID=40&md5=a9cd141e9babb4e52f087165013b9c8f http://cmuir.cmu.ac.th/handle/6653943832/6184 |
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1681420566158901248 |