| Banach空间中Reich-Takahashi迭代法的强收敛定理 |
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| 引用本文： | 曾六川.Banach空间中Reich-Takahashi迭代法的强收敛定理[J].数学学报,2005,48(3):417-426. |
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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： | 教育部高校优秀青年教师教学和科研奖励基金
上海市教委高校科技发展基金
科委重大项目基金(部分)资助
上海市曙光计划基金资助项目 |
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| 摘 要： | 设E是具有一致正规结构的实Banach空间,其范数是一致Gateaux可微的;设D是E的非空有界闭凸子集,T:D→D是渐近非扩张映象.本文证明了,在一些适当的条件下,由修正的Reich-Takahashi迭代法(1.2)式所定义的序列{xn}强收敛到渐近非扩张映象的不动点,其中x0是D中一任给点,{αn},{β}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 修正的Reich-Takahashi迭代法 |
Strong Convergence Theorems of the Modified Reich-Takahashi Iteration Method in Banach Spaces |
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| Lu Chuan ZENG.Strong Convergence Theorems of the Modified Reich-Takahashi Iteration Method in Banach Spaces[J].Acta Mathematica Sinica,2005,48(3):417-426. |
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| Authors: | Lu Chuan ZENG |
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| Institution: | Lu Chuan ZENG Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China |
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| Abstract: | Let E be a real Banach space with uniform normal structure, whose norm is uniformly Gateaux differentiable. Let D be a nonempty bounded closed convex subset of E and T : D → D be an asymptotically nonexpansive mapping. It is shown that under some suitable conditions, the sequence {xn} defined by the modified Reich-Takahashi iteration method (1.2) converges strongly to a fixed point of T, where x0 is any given point in D, and {αn}, {β} are real sequences in 0,1] with some restrictions. |
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| Keywords: | Fixed point Asymptotically nonexpansive mappings Modified Reich-Taka-hashi iteration method |
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