| 姚永红,陈汝栋.关于渐近非扩张映象不动点迭代的一点注记[J].数学研究及应用,2006,26(2):377~382 |
| 关于渐近非扩张映象不动点迭代的一点注记 |
| A Note on Approximating Fixed Points of Asymptotically Nonexpansive Mapping |
| 投稿时间：2004-02-15 |
| DOI：10.3770/j.issn:1000-341X.2006.02.026 |
| 中文关键词: 渐近非扩张映象 修改了的Ishikawa迭代程序 不动点 一致凸Banach空间. |
| 英文关键词:asymptotically nonexpansive mapping modified Ishikawa iteration process fixed point uniformly convex Banach space. |
| 基金项目:天津市高校科技发展基金(20040401) |
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| 中文摘要: |
| 设$E$是一致凸Banach空间, $C$是$E$的非空闭凸子集, $T:C\rightarrow C$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 $\{x_n\}$:$x_{n+1}=rp_n, p_n=(1-a_n)x_n+a_nT^{m_n}ry_n+u_n$, $y_n=(1-b_n)x_n+b_nT^{k_n}x_n+v_n$, $(n\geq 1)$弱收敛到$T$的不动点. |
| 英文摘要: |
| Let $E$ be a uniformly convex Banach space, $C$ be a nonempty closed convex subset of $E$, and $T:C\rightarrow C$ 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: $x_{n+1}=rp_n, p_n=(1-a_n)x_n+a_nT^{m_n}ry_n+u_n$, $y_n=(1-b_n)x_n+b_nT^{k_n}x_n+v_n$, $(n\geq 1)$ converges weakly to a fixed point of $T$. |
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