| 魏利,周海云.Banach空间中两个极大单调算子公共零点的迭代格式[J].数学研究及应用,2007,27(4):913~918 |
| Banach空间中两个极大单调算子公共零点的迭代格式 |
| An Iterative Algorithm of Common Zero Points for Two Maximal Monotone Operators in Banach Space |
| 投稿时间：2005-10-08 修订日期：2006-07-02 |
| DOI：10.3770/j.issn:1000-341X.2007.04.041 |
| 中文关键词: Lyapunov泛函 极大单调算子 一致凸Banach空间. |
| 英文关键词:Lyapunov functional maximal monotone operator uniformly convex Banach space. |
| 基金项目:国家自然科学基金(10471033). |
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| 中文摘要: |
| 令$E$为实光滑、一致凸Banach空间, $E^*$ 为其对偶空间.令$A,B \subset E \times E^*$ 为极大单调算子且 $A^{-1}0 \cap B^{-1}0 \neq \emptyset$. 本文将引入新的迭代格式,利用Lyapunov泛函与广义投影算子等技巧,证明迭代序列弱收敛于极大单调算子$A$和$B$的公共零点. |
| 英文摘要: |
| Let $E$ be a real smooth and uniformly convex Banach space with $E^*$ being its duality space. Let $A,B \subset E \times E^*$ be maximal monotone operators with $A^{-1}0\cap B^{-1}0 \neq \emptyset$. A new iterative algorithm is introduced which is proved to be weakly convergent to common zero points of maximal monotone operators $A$ and $B$ by using the techniques of Lyapunov functional and generalized projection operator, etc. |
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