Relaxed Extragradient Methods with Regularization for General System of Variational Inequalities with Constraints of Split Feasibility and Fixed Point Problems
We suggest and analyze relaxed extragradient iterative algorithms with regularization for finding a common element of the solution set of a general system of variational inequalities, the solution set of a split feasibility problem, and the fixed point set of a strictly pseudocontractive mapping def...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/891232 |
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| author | L. C. Ceng A. Petruşel J. C. Yao |
| author_facet | L. C. Ceng A. Petruşel J. C. Yao |
| author_sort | L. C. Ceng |
| collection | DOAJ |
| description | We suggest and analyze relaxed extragradient iterative algorithms with regularization for finding a common element of the solution set of a general system of variational inequalities, the solution set of a split feasibility problem, and the fixed point set of a strictly pseudocontractive mapping defined on a real Hilbert space. Here the relaxed extragradient methods with regularization are based on the well-known successive approximation method, extragradient method, viscosity approximation method, regularization method, and so on. Strong convergence of the proposed algorithms under some mild conditions is established. Our results represent the supplementation, improvement, extension, and development of the corresponding results in the very recent literature. |
| format | Article |
| id | doaj-art-8859906125824e8fb376e60b675a0484 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-8859906125824e8fb376e60b675a04842025-02-03T05:44:10ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/891232891232Relaxed Extragradient Methods with Regularization for General System of Variational Inequalities with Constraints of Split Feasibility and Fixed Point ProblemsL. C. Ceng0A. Petruşel1J. C. Yao2Department of Mathematics, Shanghai Normal University, and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, ChinaDepartment of Applied Mathematics, Babeş-Bolyai University, 400084 Cluj-Napoca, RomaniaCenter for Fundamental Science, Kaohsiung Medical University, Kaohsiung 807, TaiwanWe suggest and analyze relaxed extragradient iterative algorithms with regularization for finding a common element of the solution set of a general system of variational inequalities, the solution set of a split feasibility problem, and the fixed point set of a strictly pseudocontractive mapping defined on a real Hilbert space. Here the relaxed extragradient methods with regularization are based on the well-known successive approximation method, extragradient method, viscosity approximation method, regularization method, and so on. Strong convergence of the proposed algorithms under some mild conditions is established. Our results represent the supplementation, improvement, extension, and development of the corresponding results in the very recent literature.http://dx.doi.org/10.1155/2013/891232 |
| spellingShingle | L. C. Ceng A. Petruşel J. C. Yao Relaxed Extragradient Methods with Regularization for General System of Variational Inequalities with Constraints of Split Feasibility and Fixed Point Problems Abstract and Applied Analysis |
| title | Relaxed Extragradient Methods with Regularization for General System of Variational Inequalities with Constraints of Split Feasibility and Fixed Point Problems |
| title_full | Relaxed Extragradient Methods with Regularization for General System of Variational Inequalities with Constraints of Split Feasibility and Fixed Point Problems |
| title_fullStr | Relaxed Extragradient Methods with Regularization for General System of Variational Inequalities with Constraints of Split Feasibility and Fixed Point Problems |
| title_full_unstemmed | Relaxed Extragradient Methods with Regularization for General System of Variational Inequalities with Constraints of Split Feasibility and Fixed Point Problems |
| title_short | Relaxed Extragradient Methods with Regularization for General System of Variational Inequalities with Constraints of Split Feasibility and Fixed Point Problems |
| title_sort | relaxed extragradient methods with regularization for general system of variational inequalities with constraints of split feasibility and fixed point problems |
| url | http://dx.doi.org/10.1155/2013/891232 |
| work_keys_str_mv | AT lcceng relaxedextragradientmethodswithregularizationforgeneralsystemofvariationalinequalitieswithconstraintsofsplitfeasibilityandfixedpointproblems AT apetrusel relaxedextragradientmethodswithregularizationforgeneralsystemofvariationalinequalitieswithconstraintsofsplitfeasibilityandfixedpointproblems AT jcyao relaxedextragradientmethodswithregularizationforgeneralsystemofvariationalinequalitieswithconstraintsofsplitfeasibilityandfixedpointproblems |