朱兰萍,李刚.空间中渐近非扩张型映射的渐近行为[J].数学研究及应用,2009,29(1):129~136 |
空间中渐近非扩张型映射的渐近行为 |
Asymptotic Behavior of Asymptotically Nonexpansive Type Mappings in Banach Space |
投稿时间:2006-12-14 修订日期:2007-07-13 |
DOI:10.3770/j.issn:1000-341X.2009.01.017 |
中文关键词: 渐近非扩张型映射 Kadec-Klee性质 定向网 渐近行为. |
英文关键词:asymptotically nonexpansive type mappings Kadec-Klee property directed system asymptotic behavior. |
基金项目:国家自然科学基金(No.10571150);江苏省教育厅自然科学基金(No.07KJB110131);杨州大学自然科学基金(No.FK0513101). |
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中文摘要: |
设$X$为一致凸Banach空间,且其对偶空间$X^*$具有KK性质.$C$为$X$的非空有界闭凸子集,$G$ 为一定向网. 设$\Im=\{T_{t}:t\in{G}\}$为$C$上一族渐近非扩张型映射.本文主要考察了$\{T_{t}x_0:t\in{G}\}$的渐近行为同时给出了其弱收敛定理. |
英文摘要: |
Let $X$ be a uniformly convex Banach space $X$ such that its dual $X^*$ has the KK property. Let $C$ be a nonempty bounded closed convex subset of $X$ and $G$ be a directed system. Let $\Im=\{T_{t}: t\in{G}\}$ be a family of asymptotically nonexpansive type mappings on $C$. In this paper, we investigate the asymptotic behavior of $\{T_{t}x_0: t\in{G}\}$ and give its weak convergence theorem. |
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