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 |
Banach空间中含$(H,\eta)$单调算子变分包含组解的迭代法 |
Iterative Methods for Solving a System of Variational Inclusions Involving $(H,\eta)$-Monotone Operators in Banach Spaces |
投稿时间:2007-01-29 修订日期:2007-07-13 |
DOI:10.3770/j.issn:1000-341X.2009.01.005 |
中文关键词: $q$-一致光滑Banach空间 $(H,\eta)$-单调算子 予解算子方法 变分包含组 迭代算法. |
英文关键词:$q$-uniformly smooth space $(H, \eta)$-monotone operator Resolvent operator technique system of variational inclusion iterative algorithm. |
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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中文摘要: |
本文中,我们在Banach空间定义和研究了一类含有$(H,\eta)$-单调算子的新的变分包含组.利用$(H,\eta)$-单调算子予解式的性质,我们证明了该变分包含组解的存在及唯一性,并构造了逼近这个变分包含组解的迭代算法.最后讨论了由该算法生成的迭代序列收敛性问题. |
英文摘要: |
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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