关于Banach空间中渐近非扩张映象的几乎轨道的渐近行为(英文)

On the Asymptotic Behavior of Almost-orbits of Asymptotically Non-expansive Mappings in Banach Spaces

设X是一致凸Banach空间，且满足Opial条件或其范教是Frechet可微的，C是X的有界闭凸子集，T：C→C渐近非扩张映象。证明了，若序列是T的几乎轨道且满足，则，弱收敛到T的一个不动点。

Let X be a uniformly convex Banach space which satisfies Opial's condition or whose norm is Frechet differentiable, C be a bounded closed convex subset of X, and T: C→C be an asymptotically nonexpansive mapping. It is proven that if {xn}∞n=0 is an almostorbit of T satisfyinglimm→∞lim supn→∞||xn+m - xn ||= 0then the Sequence {xn} convcyes weakly to a fixed point of T.