关于增生算子方程解的带误差的Ishikawa迭代程序

数学物理学报 ›› 2004, Vol. 4 ›› Issue (6): 654-660.

关于增生算子方程解的带误差的Ishikawa迭代程序

曾六川

上海师范大学数学系

出版日期:2004-12-25 发布日期:2004-12-25
基金资助:
高等学校优秀青年教师教学和科研奖励基金、上海市高校科技发展基金(部分)和上海市曙光计划基金

Ishikawa Iteration Process with Errors for Solutions to Equations Involving Accretive Operators

CENG Liu-Chuan

Shanghai Normal University

Online:2004-12-25 Published:2004-12-25
Supported by:
高等学校优秀青年教师教学和科研奖励基金、上海市高校科技发展基金(部分)和上海市曙光计划基金

摘要/Abstract

摘要：

该文在Banach空间中证明了，带误差的Ishikawa迭代序列强收敛到Lipschitz连续的增生算子方程的唯一解．而且，也给Ishikawa迭代序列提供了一般的收敛率估计．利用该结果还推得，带误差的Ishikawa迭代序列也强收敛到Lipschitz连续的强增生算子方程的唯一解．

关键词: 任意实Banach空间, 增生算子, 带误差的Ishikawa迭代序列, 收敛率估计

Abstract:

It is shown that the Ishikawa iterative sequence with errors converges strongly to the unique solution of the equation involving the Lipschitz continuous accretive operator in a Banach space. Moreover, our result provides a general convergence rate estimate for the Ishikawa iterative sequence. From this result, it follows that the Ishikawa iterative sequence with errors alsoconverges strongly to the unique solution of the equation of the Lipschitz continuous strongly accretive operator.

Key words: Arbitrary real Banach space, Accretive operator, Ishikawa iterative sequence with errors, Convergence rate estimate.

中图分类号:

47H09

曾六川. 关于增生算子方程解的带误差的Ishikawa迭代程序[J]. 数学物理学报, 2004, 4(6): 654-660.

CENG Liu-Chuan. Ishikawa Iteration Process with Errors for Solutions to Equations Involving Accretive Operators[J]. Acta mathematica scientia,Series A, 2004, 4(6): 654-660.

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