Implicit and Explicit Iterative Methods for Systems of Variational Inequalities and Zeros of Accretive Operators
Based on Korpelevich's extragradient method, hybrid steepest-descent method, and viscosity approximation method, we propose implicit and explicit iterative schemes for computing a common element of the solution set of a system of variational inequalities and the set of zeros of an accretive ope...
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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/10.1155/2013/631382 |
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| _version_ | 1832566997454422016 |
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| author | Lu-Chuan Ceng Saleh Abdullah Al-Mezel Qamrul Hasan Ansari |
| author_facet | Lu-Chuan Ceng Saleh Abdullah Al-Mezel Qamrul Hasan Ansari |
| author_sort | Lu-Chuan Ceng |
| collection | DOAJ |
| description | Based on Korpelevich's extragradient method, hybrid steepest-descent method, and viscosity approximation method, we propose implicit and explicit iterative schemes for computing a common element of the solution set of a system of variational inequalities and the set of zeros of an accretive operator, which is also a unique solution of a variational inequality. Under suitable assumptions, we study the strong convergence of the sequences generated by the proposed algorithms. The results of this paper improve and extend several known results in the literature. |
| format | Article |
| id | doaj-art-e3489fbedf624fa190161cc7af94185c |
| 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-e3489fbedf624fa190161cc7af94185c2025-02-03T01:02:35ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/631382631382Implicit and Explicit Iterative Methods for Systems of Variational Inequalities and Zeros of Accretive OperatorsLu-Chuan Ceng0Saleh Abdullah Al-Mezel1Qamrul Hasan Ansari2Department of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaBased on Korpelevich's extragradient method, hybrid steepest-descent method, and viscosity approximation method, we propose implicit and explicit iterative schemes for computing a common element of the solution set of a system of variational inequalities and the set of zeros of an accretive operator, which is also a unique solution of a variational inequality. Under suitable assumptions, we study the strong convergence of the sequences generated by the proposed algorithms. The results of this paper improve and extend several known results in the literature.http://dx.doi.org/10.1155/2013/631382 |
| spellingShingle | Lu-Chuan Ceng Saleh Abdullah Al-Mezel Qamrul Hasan Ansari Implicit and Explicit Iterative Methods for Systems of Variational Inequalities and Zeros of Accretive Operators Abstract and Applied Analysis |
| title | Implicit and Explicit Iterative Methods for Systems of Variational Inequalities and Zeros of Accretive Operators |
| title_full | Implicit and Explicit Iterative Methods for Systems of Variational Inequalities and Zeros of Accretive Operators |
| title_fullStr | Implicit and Explicit Iterative Methods for Systems of Variational Inequalities and Zeros of Accretive Operators |
| title_full_unstemmed | Implicit and Explicit Iterative Methods for Systems of Variational Inequalities and Zeros of Accretive Operators |
| title_short | Implicit and Explicit Iterative Methods for Systems of Variational Inequalities and Zeros of Accretive Operators |
| title_sort | implicit and explicit iterative methods for systems of variational inequalities and zeros of accretive operators |
| url | http://dx.doi.org/10.1155/2013/631382 |
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