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

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∩∞ｎ＝１ｃｏ｛ｘｉ：ｉ≥ｎ｝∩Ｆ（Ｔ）的唯一点，其中，Ｆ（Ｔ）是Ｔ的不动点集．

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:n≥1} is an almost orbit of T, then the sequence {x n} is weakly almost convergent to the unique point of the set ∩∞n=1 co {x i:i≥n}∩F(T), where F(T) is the fixed point set of T.