曾六川.关于增生算子方程解的Ishikawa迭代逼近[J].数学研究及应用,2005,25(1):92~98 |
关于增生算子方程解的Ishikawa迭代逼近 |
Ishikawa Iterative Approximations of Solutions to Equations Involving Accretive Operators |
投稿时间:2002-03-29 |
DOI:10.3770/j.issn:1000-341X.2005.01.013 |
中文关键词: 任意实Banach空间 增生算子 带误差的Ishikawa迭代序列 收敛率估计 |
英文关键词:arbitrary real Banach space accretive operator Ishikawa iterative sequence with errors convergence rate estimate |
基金项目:国家教育部高等学校优秀青年教师教学和科研奖励基金,上海市曙光计划基金 |
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中文摘要: |
设X是任意实Banach空间,T:X→X是Lipschitz连续的增生算子.本文证明了,带误差的Ishikawa迭代序列强收敛到方程x+Tx=f的唯一解.而且,还给Ishikawa迭代序列提供了一般的收敛率估计.利用该结果,本文推得,若T:X→X是Lipschitz连续的强增生算子,则带误差的Ishikawa迭代序列强收敛到方程Tx=f的唯一解. |
英文摘要: |
Let X be an arbitrary real Banach space and T : X →X be a Lipschitz continuous accretive operator. It is shown that the Ishikawa iterative sequence with errors converges strongly to the unique solution of the equation x+Tx =f. Moreover, our result provides a general convergence rate estimate for the Ishikawa iterative sequence. Utilizing this result, we show that if T : X →X is a Lipschitz continuous strongly accretive operator, then the Ishikawa iterative sequence with errors converges strongly to the unique solution of the equation Tx=f. |
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