曾六川.一致凸Banach空间中渐近非扩张映象的几乎轨道的渐近行为[J].数学研究及应用,1998,18(1):96~98
一致凸Banach空间中渐近非扩张映象的几乎轨道的渐近行为
Asymptotic Behaviour of Almost Orbits of Asymptotically Nonexpansive Mappings in Uniformly Convex Banach Spaces
投稿时间:1993-11-01  
DOI:10.3770/j.issn:1000-341X.1998.01.017
中文关键词:  几乎轨道  渐近非扩张映象  不动点  弱几乎收敛
英文关键词:almost orbit  asymptotically nonexpansive mapping  weakly almost convergent.
基金项目:
作者单位
曾六川 上海师范大学数学系
复旦大学数学所 
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中文摘要:
      设X是有Fréchet可微范数的一致凸Banach空间,C是X的有界闭凸子集,T:C→C是一个渐近非扩张映象.证明了,如果{x:n≥1}是T的几乎轨道,则序列{x0}弱几乎收敛到集合∩from∞to(n=1)co{xi:i≥n}∩F(T)的唯一点,其中,F(T)是T的不动点集.
英文摘要:
      Let X be a uniformly convex Banach space with a Fréchet differentiable norm, C a bounded closed convex subset of X and T:C→C an asymptotically nonexpansive mapping. It is shown that if {x:n≥1} is an almost orbit of T, then the sequence {x n} is weakly almost convergent to the unique point of the set ∩from∞to (n=1) co {xi:i≥n}∩F(T), where F(T) is the fixed point set of T.
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