| 关于Banach空间中增生算子方程的迭代法收敛率估计 |
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| 引用本文： | 曾六川.关于Banach空间中增生算子方程的迭代法收敛率估计[J].应用数学,2002,15(2):80-84. |
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| 作者姓名： | 曾六川 |
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| 作者单位： | 上海师范大学数学系,上海,200234 |
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| 基金项目： | ProjectsupportedbothbytheTeachingandResearchAwardFundforOutstandingYoungTeachersinHigherEducationInstitutionsofMOE，P .R.C，theNationalNaturalScienceFoundation(1980 10 2 3)，P .R .C . |
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| 摘 要： | 本文研究Banach空间中增生算子方程的Ishikawa迭代法收敛率估计。本文所得结果在以下方面改进和推广了刘理蔚的结果（Nonlinear Anal.42(2)(2000),271-276):(1)以假设{αn},{βn}在不同区间上独立取值代替刘的假设limn→∞αn=limn→∞βn＝0；（2）以一般的收敛率估计和几何收敛率估计代替刘的收敛率估计||xm=x^*||=O(1/m）。
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| 关 键 词： | Banach空间 增生算子方程 收敛率估计 Ishikawa迭代法 几何收敛率 |
On the Convergence Rate Estimates of Iteration Methods for Equations Involving Accretive Operators in Banach Spaces |
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| ZENG Liu-chuan.On the Convergence Rate Estimates of Iteration Methods for Equations Involving Accretive Operators in Banach Spaces[J].Mathematica Applicata,2002,15(2):80-84. |
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| Authors: | ZENG Liu-chuan |
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| Abstract: | The purpose of this paper is to investigate the convergence rate estimate of Ishikawa iteration method for equations involving accretive operators in Banach spaces. The results presented in this paper improve and extend Lius result (Nonlinear Anal. 42(2)(2000),271-276) through replacing Lius assumption that limαn = limβn = 0 by the assumption that {αn }, {βn } independently take values in the different intervals, and through replacing Lius convergence rate estimate ‖ xm -x* ‖}= O(1/m) by the general convergence rate estimate and the geometric convergence rate estimate. |
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| Keywords: | Accretive operator Ishikawa iteration method Convergence rate estimate |
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