| 魏利,周海云.Banach空间中极大单调算子零点的迭代逼近定理[J].数学研究及应用,2007,27(1):177~184 |
| Banach空间中极大单调算子零点的迭代逼近定理 |
| A Theorem of Iterative Approximation of Zero Point for Maximal Monotone Operator in Banach Space |
| 投稿时间：2005-02-25 修订日期：2005-07-17 |
| DOI：10.3770/j.issn:1000-341X.2007.01.024 |
| 中文关键词: Lyapunov泛函 极大单调算子 一致凸Banach空间 Reich不等式. |
| 英文关键词:Lyapunov functional maximal monotone operator uniformly convex Banach space Reich inequality. |
| 基金项目:国家自然科学基金(10471003) |
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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$A \subset E \times E^*$ 为极大单调算子, $A^{-1}0 \neq \phi$.本文将引入新的迭代算法, 并利用Lyapunov泛函, $Q_r$算子与广义投影算子等技巧,证明了迭代序列弱收敛于极大单调算子$A$的零点的结论. |
| 英文摘要: |
| Let $E$ be a real smooth and uniformly convex Banach space, and $E^*$ its duality space. Let $A \subset E \times E^*$ be a maximal monotone operator with $A^{-1}0 \neq \phi$. A new iterative scheme is introduced which is proved to be weakly convergent to zero point of maximal monotone operator $A$ by using the techniques of Lyapunov functional, $Q_r$ operator and generalized projection operator, etc. |
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