| 关于非线性算子不动点收敛定理等价性的探讨 |
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| 引用本文： | 薛志群,范瑞琴.关于非线性算子不动点收敛定理等价性的探讨[J].石家庄铁道学院学报,2007,20(4):54-56. |
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| 作者姓名： | 薛志群 范瑞琴 |
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| 作者单位： | 石家庄铁道学院数理系,河北石家庄050043 |
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| 摘 要： | 在适当放宽不动点定理的条件下，分别证明了Picard迭代序列与Mann迭代序列收敛定理的等价性以及Mann迭代序列与Ishikawa迭代序列收敛定理的等价性。
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| 关 键 词： | Z算子 不动点 Picard迭代序列 Mann迭代序列 Ishikawa迭代序列 |
| 文章编号： | 1674-0300（2007）04-0054-03 |
| 收稿时间： | 2007-10-12 |
| 修稿时间： | 2007年10月12 |
The Equivalence of Convergence Theorems for Fixed Point of Nonlinear Operator |
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| Xue Zhiqun,Fan Ruiqin.The Equivalence of Convergence Theorems for Fixed Point of Nonlinear Operator[J].Journal of Shijiazhuang Railway Institute,2007,20(4):54-56. |
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| Authors: | Xue Zhiqun Fan Ruiqin |
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| Institution: | Department of Mathematics and Physics, Shijiazhuang Railway Institute, Shijiazhuang 050043 ,China |
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| Abstract: | In this paper, it is shown that the convergence of Picard iteration sequence is equivalent to Mann iteration sequence, and the convergence of Mann iteration sequence is equivalent to Ishikawa iteration sequence for Zamfirescu operators in an arbitrary Banach space. |
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| Keywords: | Zamfirescu operator fixed point Picard iteration sequence Mann iteration sequence Ishikawa iteration sequence |
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