| Banach空间中含$(H,eta)$单调算子变分包含组解的迭代法 |
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| 引用本文： | 娄健,何欣枫,何震. Banach空间中含$(H,eta)$单调算子变分包含组解的迭代法[J]. 数学研究及应用, 2009, 29(1): 33-42 |
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| 作者姓名： | 娄健 何欣枫 何震 |
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| 作者单位： | 河北大学计算中心, 河北 保定 071002;河北大学数学与计算机学院, 河北 保定 071002;河北大学数学与计算机学院, 河北 保定 071002 |
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| 基金项目： | 教育部科学技术研究重点项目(No.207104); 河北省自然科学基金(No.A2006000941). |
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| 摘 要： | In this paper, we introduce and study a new system of variational inclusions involving （H, η）-monotone operators in Banach space. Using the resolveut operator associated with （H, η）- monotone operators, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the iterative sequence generated by the algorithm.
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| 关 键 词： | 非线性 泛函分析 算子 空间理论 |
| 收稿时间： | 2007-01-29 |
| 修稿时间： | 2007-07-13 |
Iterative Methods for Solving a System of Variational Inclusions Involving $(H,eta)$-Monotone Operators in Banach Spaces |
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| LOU Jian,HE Xin Feng and HE Zhen. Iterative Methods for Solving a System of Variational Inclusions Involving $(H,eta)$-Monotone Operators in Banach Spaces[J]. Journal of Mathematical Research with Applications, 2009, 29(1): 33-42 |
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| Authors: | LOU Jian HE Xin Feng HE Zhen |
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| Affiliation: | Computer Center, Hebei University, Hebei 071002, China;College of Mathematics and Computers, Hebei University, Hebei 071002, China;College of Mathematics and Computers, Hebei University, Hebei 071002, China |
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| Abstract: | In this paper, we introduce and study a new system of variational inclusions involving $(H, eta)$-monotone operators in Banach space. Using the resolvent operator associated with $(H, eta)$- monotone operators, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the iterative sequence generated by the algorithm. |
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| Keywords: | $q$-uniformly smooth space $(H, eta)$-monotone operator Resolvent operator technique system of variational inclusion iterative algorithm. |
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