| 赵良才,张石生.Banach空间中非扩张映象不动点的黏性逼近[J].数学研究及应用,2007,27(4):919~924 |
| Banach空间中非扩张映象不动点的黏性逼近 |
| Viscosity Approximtion of Fixed Points for Nonexpansive Mappings in Banach Spaces |
| 投稿时间：2005-09-29 修订日期：2006-07-02 |
| DOI：10.3770/j.issn:1000-341X.2007.04.042 |
| 中文关键词: 不动点 压缩映象 非扩张映象 黏性逼近. |
| 英文关键词:fixed point contractive mapping nonexpansive mapping viscosity approximation. |
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| 中文摘要: |
| 设$E$是一致光滑的Banach空间,其范数是一致Gateaux可微的;设$C$是$E$之一非空闭凸子集, $f:C\to C$是压缩映象, $T:C\to C$是非扩张映象.本文用黏性逼近方法证明了在较一般的条件下,由(1.6)式定义的迭代序列$\{x_n\}$的强收敛性.本文推广和改进了一些近期结果. |
| 英文摘要: |
| Let $E$ be a uniformly smooth Banach space, whose norm is uniformly Gateaux differentiable. Let $C$ be a closed convex subset of $E$, $f:C\rightarrow C$ be a contractive mapping, and $T:C\rightarrow C$ be a nonexpansive mapping. It is shown that under more general contractions of viscosity approximation methods, the sequence $\{x_n\}$ defined by (1.6) converges strongly. The results presented in this paper also extend and improve some recent results. |
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