Generalized H-η-accretive operators in Banach spaces with application to variational inclusions |
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引用本文: | 罗雪萍,黄南京.Generalized H-η-accretive operators in Banach spaces with application to variational inclusions[J].应用数学和力学(英文版),2010,31(4):501-510. |
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作者姓名: | 罗雪萍 黄南京 |
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作者单位: | Department of Mathematics,Sichuan University,Chengdu 610064,P.R.China |
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基金项目: | the National Natural Science Foundation of China,the Key Program of the National Natural Science Foundation of China,the Specialized Research Fund for the Doctoral Program of Higher Education |
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摘 要: | In this paper, a new notion of a generalized H-η-accretive operator is introduced and studied, which provides a unifying framework for the generalized m-accretive operator and the H-η-monotone operator in Banach spaces. A resolvent operator associated with the generalized H-η-accretive operator is defined, and its Lipschitz continuity is shown. As an application, the solvability for a class of variational inclusions involving the generalized H-η-accretive operators in Banach spaces is considered. By using the technique of the resolvent mapping, an iterative algorithm for solving the variational inclusion in Banach spaces is constructed. Under some suitable conditions, it is proven that the solution for the variational inclusion and the convergence of the iterative sequence generated by the algorithm exist.
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关 键 词: | Banach空间 增生算子 变分包含 广义 Lipschitz连续性 应用 迭代算法 单调算子 |
收稿时间: | 2009-06-15 |
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