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. |
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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{xn: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 {xn: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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