| Banach空间中极大单调算子零点的迭代逼近定理 |
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| 引用本文： | 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].数学研究与评论,2007,27(1):177-184. |
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| 作者姓名： | 魏利 周海云 |
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| 作者单位： | 1. 河北经贸大学数学与统计学学院,河北,石家庄,050061;军械工程学院应用数学与力学研究所,河北,石家庄,050003
2. 军械工程学院应用数学与力学研究所,河北,石家庄,050003;河北师范大学数学与信息科学学院,河北,石家庄,050016 |
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| 摘 要： | 令E为实光滑、一致凸Banach空间,E为其对偶空间．令A■ E x E为极大单调算子, A-10≠■．本文将引入新的迭代算法,并利用Lyapunov泛函, Qr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．
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| 关 键 词： | Lyapunov泛函 极大单调算子 一致凸Banach空间 Reich不等式 |
| 文章编号： | 1000-341X(2007)01-0177-08 |
| 收稿时间： | 2005/2/25 0:00:00 |
| 修稿时间： | 02 25 2005 12:00AM |
A Theorem of Iterative Approximation of Zero Point for Maximal Monotone Operator in Banach Space |
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| WEI Li and ZHOU Hai-yun.A Theorem of Iterative Approximation of Zero Point for Maximal Monotone Operator in Banach Space[J].Journal of Mathematical Research and Exposition,2007,27(1):177-184. |
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| Authors: | WEI Li and ZHOU Hai-yun |
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| Institution: | School of Mathematics and Statistics, Hebei University of Economics and Business, Hebei 050061, China; Institute of Applied Mathematics and Mechanics, Ordnance Engineering College, Hebei 050003, China;Institute of Applied Mathematics and Mechanics, Ordnance Engineering College, Hebei 050003, China; Institute of Mathematics and Information Sciences, Hebei Normal University, Hebei 050016, China |
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| Abstract: | 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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| Keywords: | Lyapunov functional maximal monotone operator uniformly convex Banach space Reich inequality |
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