| Asymptotic Behavior of Asymptotically Nonexpansive Type Mappings in Banach Space |
| Received:December 14, 2006 Revised:July 13, 2007 |
| Key Words:
asymptotically nonexpansive type mappings Kadec-Klee property directed system asymptotic behavior.
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| Fund Project:the National Natural Science Foundation of China (No.10571150); the Natural Science Foundation of Jiangsu Education Committee of China (No.07KJB110131) and the Natural Science Foundation of Yangzhou University (No.FK0513101). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2009.01.017 |
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