Existence and Iterative Algorithm of Solutions for a System of Generalized Nonlinear Mixed Variational-Like Inequalities
We introduce and study a system of generalized nonlinear mixed variational-like inequality problems (SGNMVLIPs) in Banach spaces. The auxiliary principle technique is applied to study the existence and iterative algorithm of solutions for the SGNMVLIP. First, the existence of solutions of the auxili...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/176283 |
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| author | Yan-Mei Du |
| author_facet | Yan-Mei Du |
| author_sort | Yan-Mei Du |
| collection | DOAJ |
| description | We introduce and study a system of generalized nonlinear mixed variational-like inequality problems (SGNMVLIPs) in Banach spaces. The auxiliary principle technique is applied to study the existence and iterative algorithm of solutions for the SGNMVLIP. First, the existence of solutions of the auxiliary problems for the SGNMVLIP is shown. Second, an iterative algorithm for solving the SGNMVLIP is constructed by using this existence result. Finally, not only the existence of solutions of the SGNMVLIP is shown but also the convergence of iterative sequences generated by the algorithm is also proven. The technique and results presented in this paper generalize and unify the corresponding techniques and results given in the literature. |
| format | Article |
| id | doaj-art-27107dbd94284be5b350a7dd9fe73e24 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-27107dbd94284be5b350a7dd9fe73e242025-02-03T06:07:00ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/176283176283Existence and Iterative Algorithm of Solutions for a System of Generalized Nonlinear Mixed Variational-Like InequalitiesYan-Mei Du0Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, ChinaWe introduce and study a system of generalized nonlinear mixed variational-like inequality problems (SGNMVLIPs) in Banach spaces. The auxiliary principle technique is applied to study the existence and iterative algorithm of solutions for the SGNMVLIP. First, the existence of solutions of the auxiliary problems for the SGNMVLIP is shown. Second, an iterative algorithm for solving the SGNMVLIP is constructed by using this existence result. Finally, not only the existence of solutions of the SGNMVLIP is shown but also the convergence of iterative sequences generated by the algorithm is also proven. The technique and results presented in this paper generalize and unify the corresponding techniques and results given in the literature.http://dx.doi.org/10.1155/2012/176283 |
| spellingShingle | Yan-Mei Du Existence and Iterative Algorithm of Solutions for a System of Generalized Nonlinear Mixed Variational-Like Inequalities Journal of Applied Mathematics |
| title | Existence and Iterative Algorithm of Solutions for a System of Generalized Nonlinear Mixed Variational-Like Inequalities |
| title_full | Existence and Iterative Algorithm of Solutions for a System of Generalized Nonlinear Mixed Variational-Like Inequalities |
| title_fullStr | Existence and Iterative Algorithm of Solutions for a System of Generalized Nonlinear Mixed Variational-Like Inequalities |
| title_full_unstemmed | Existence and Iterative Algorithm of Solutions for a System of Generalized Nonlinear Mixed Variational-Like Inequalities |
| title_short | Existence and Iterative Algorithm of Solutions for a System of Generalized Nonlinear Mixed Variational-Like Inequalities |
| title_sort | existence and iterative algorithm of solutions for a system of generalized nonlinear mixed variational like inequalities |
| url | http://dx.doi.org/10.1155/2012/176283 |
| work_keys_str_mv | AT yanmeidu existenceanditerativealgorithmofsolutionsforasystemofgeneralizednonlinearmixedvariationallikeinequalities |