| 关于非扩张映象的不动点逼近的Ishikawa迭代程序 |
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| 引用本文： | 曾六川. 关于非扩张映象的不动点逼近的Ishikawa迭代程序[J]. 数学研究及应用, 2003, 23(1): 33-39 |
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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： | Supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE,China. |
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| 摘 要： | 设E是一致凸Banach空间,满足Opial条件或具有Frechet可微范数.又设C是E的有界闭凸子集.若T:C→C是非扩张映象,则对任给的初始数据x0∈C,由Ishikawa迭代程序xn+1=tnT(snTxn+(1-sn)xn)+(1-tn)xn,n≥0,定义的序列{xn}弱收敛到T的
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| 关 键 词： | 非扩张映象 不动点逼近 Ishikawa迭代程序 |
| 收稿时间： | 2000-04-03 |
Ishikawa Iteration Process for Approximating Fixed Points of Nonexpansive Mappings |
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| ZENG Lu-chuan. Ishikawa Iteration Process for Approximating Fixed Points of Nonexpansive Mappings[J]. Journal of Mathematical Research with Applications, 2003, 23(1): 33-39 |
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| Authors: | ZENG Lu-chuan |
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| Affiliation: | Dept. of Math.; Shanghai Normal University; Shanghai; China |
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| Abstract: | LetE be a uniformly convex Banach space which satisfies Opial's condition or has a Frechet differentiable norm, and C be a bounded closed convex subset of E. If T: C → C is a nonexpansive mapping, then for any initial data x0 ∈ C, the Ishikawa iteration process {xn}, defined by xn = tnT(snTxn + (1 - sn)xn) + (1 - tn)xn,n ≥ 0,converges weakly to a fixed point of T, where {tn} and {sn} are sequences in [0, 1] with some restrictions. |
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| Keywords: | fixed point nonexpansive mapping Ishikawa iteration process uniformly convex Banach space. |
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