| 饶若峰.涉及无限族非扩张映象$\{T_n\}_{n=1}^\infty$的迭代算法$x_{n 1}=\alpha_{n 1}f(x_n) (1-\alpha_{n 1})T_{n 1}x_n$[J].数学研究及应用,2009,29(4):639~648 |
| 涉及无限族非扩张映象$\{T_n\}_{n=1}^\infty$的迭代算法$x_{n 1}=\alpha_{n 1}f(x_n) (1-\alpha_{n 1})T_{n 1}x_n$ |
| Iteration $x_{n 1}=\alpha_{n 1}f(x_n) (1-\alpha_{n 1})T_{n 1}x_n$ for an Infinite Family of Nonexpansive Maps $\{T_n\}_{n=1}^\infty$ |
| 投稿时间：2007-05-07 修订日期：2008-03-08 |
| DOI：10.3770/j.issn:1000-341X.2009.04.009 |
| 中文关键词: 限族非扩张映象 压缩映象 弱序列连续的正规对偶映象. |
| 英文关键词:infinitely many nonexpansive mappings contractive mapping weakly sequential continuity. |
| 基金项目:四川省教育厅青年基金(No.2006Q01);基金宜宾学院基金(No.2006Q01). |
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| 中文摘要: |
| 2006年,张石生在一致光滑的Banach空间框架下证明了由$x_0\in C$ 和迭代式 $x_{n 1}= \alpha_{n 1}f(x_n) (1-\alpha_{n 1})T_{n 1}x_n$给出的序列$\{x_n\}$ 强收敛于有限族非扩张映象$\{T_n\}$的一公共不动点, 其中$f: C\to C$ 是一给定压缩映象.在本文, 作者考虑更一般的情况: $\{T_n\}$是一无穷可数族非扩张映象, 并在具弱序列连续的对偶映象的自反Banach空间框架下获得张的同样结果. |
| 英文摘要: |
| Under the framework of uniformly smooth Banach spaces, Chang$^{[1]}$ proved in 2006 that the sequence $\{x_n\}$ generated by the iteration $x_{n 1}= \alpha_{n 1}f(x_n) (1-\alpha_{n 1})T_{n 1}x_n$ converges strongly to a common fixed point of a finite family of nonexpansive maps $\{T_n\}$, where $f: C\to C$ is a contraction. However, in this paper, the author considers the iteration in more general case that $\{T_n\}$ is an infinite family of nonexpansive maps, and proves that Chang's result holds still in the setting of reflexive Banach spaces with the weakly sequentially continuous duality mapping. |
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