| Banach空间中增生算子方程迭代法与非线性收缩半群弱收敛的充要条件 |
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| 引用本文： | 蒋耀林,徐宗本.Banach空间中增生算子方程迭代法与非线性收缩半群弱收敛的充要条件[J].数学学报,1994,37(6):842-851. |
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| 作者姓名： | 蒋耀林 徐宗本 |
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| 作者单位： | 安交通大学工程力学所，西安交通大学数学系 |
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| 摘 要： | 本文在条件（Ｉ）下，证明了增生算子最速下降法和预解式迭代法弱收敛于零点的充要条件，以及非线性收缩半群弱收敛于平衡点的充要条件．所获结果推广了［１］中的基本定理，并与［２］所获得的相应强收敛充要条件对应．
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| 关 键 词： | Banach空间，增生算子迭代法，非线性收缩半群，弱收敛 |
| 收稿时间： | 1991-10-8 |
| 修稿时间： | 1993-11-15 |
A Necessary and Sufficient Condit ion for Weak Convergence of Iterative Methodsfor Accretive Operators and of Nonlinear Contraction Semigroups in Banach Spaces |
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| Jiang Yaolin.A Necessary and Sufficient Condit ion for Weak Convergence of Iterative Methodsfor Accretive Operators and of Nonlinear Contraction Semigroups in Banach Spaces[J].Acta Mathematica Sinica,1994,37(6):842-851. |
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| Authors: | Jiang Yaolin |
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| Institution: | Jiang Yaolin(Institute of Engineering Mechanics,Xi’an Jiaotong University,xi’an 710049,China)Xu Zongben(Department of Mathematics,Xi’an Jiaotong University,Xi’an 71009, China) |
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| Abstract: | A necessary and sufficient condition is presented which ensures the weak convergenceof the steepest descent and the resolvent iterations to accretive operators and of the contractionsemigroups in Banach spaces.The conclusion, which can be regarded as a weakly topologicalversion of the theorem established in2] , generalizes and improves on those results proved in1]. |
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| Keywords: | Banach space iterative met hods for accretive operators nonlinear contractionsemigroups weak Convergence |
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