Asymptotic Behavior of Asymptotically Nonexpansive Type Mappings in Banach Space
Received:December 14, 2006  Revised:July 13, 2007
Key Word: asymptotically nonexpansive type mappings   Kadec-Klee property   directed system   asymptotic behavior.  
Fund ProjectL: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).
Author NameAffiliation
ZHU Lan Ping College of Mathematics, Yangzhou University, Jiangsu 225002, China 
LI Gang College of Mathematics, Yangzhou University, Jiangsu 225002, China 
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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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