| 逼近Banach空间中渐近非扩张映象的不动点 |
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| 引用本文： | 曾六川. 逼近Banach空间中渐近非扩张映象的不动点[J]. 数学物理学报(A辑), 2003, 23(1): 31-37 |
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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： | 国家自然科学基金资助项目 (1 980 1 0 2 3 )，高等学校优秀青年教师教学和科研奖励基金资助项目，上海市科委基金 (部分 )资助项目 |
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| 摘 要： | 设E是一致凸Banach空间,C是E的非空闭凸子集, T:C→C是具有不动点的渐近非扩张映象. 该文证明了, 在某些适当的条件下, 由下列修改了的Ishikawa迭代程序所定义的序列{x-n},$$x-{n+1}=t-nT+n(s-nT+nx-n+(1-s-n)x-n)+(1-t-n)x-n,$$弱收敛到T的不动点, 其中{t-n},{s-n}是区间[0,1]中满足某些限制的实数列.
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| 关 键 词： | 不动点 渐近非扩张映象 修改了的Ishikawa迭代程序 一致凸Banach空间 |
| 文章编号： | 1003-3998(2003)01-031-07 |
Approximating Fixed Points of Asymptotically Nonexpansive Mappings in Banach Spaces |
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| Zeng Liuchuan. Approximating Fixed Points of Asymptotically Nonexpansive Mappings in Banach Spaces[J]. Acta Mathematica Scientia, 2003, 23(1): 31-37 |
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| Authors: | Zeng Liuchuan |
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| Abstract: | Let E be a uniformly convex Banach space, $C$ be a nonempty closed convexsubset of $E$, and $T:C→C$ be an asymptotically nonexpansive mapping with fixed points. It is shown that under some suitable conditions, the sequence ${x-n}$ defined by the modified Ishikawa iteration process: $$x-{n+1}=t-nT+n(s-nT+nx-n+(1-s-n)x-n)+(1-t-n)x-n,$$converges weakly to a fixed point of $T$, where ${t-n}$ and ${s-n}$ aresequences in [0,1] with some restrictions. |
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| Keywords: | Fixed point Asymptotically nonexpansive mapping Modified Ishikawa iteration process Uniformly convex Banach space. |
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