关于一致凸Banach空间中渐近非扩张半群的几乎轨道的渐近行为

On the Asymptotic Behavior of Almost-orbits of Asymptotically Nonexpansive Semigroups in Uniformly Convex Banach Spaces

设Ｘ是具有Ｆｒｃｈｅｔ可微范数的一致凸Ｂａｎａｃｈ空间，Ｃ是Ｘ的有界闭凸子集，Ｓ＝｛Ｔ（ｔ）：ｔ≥０｝是Ｃ上渐近非扩张牛群．若ｕ（·）：［０，＋∞）→Ｃ是Ｓ的几乎轨道且关于ｔ∈［０，＋∞）一致连续，则｛ｕ（ｔ）｝几乎弱收敛到集合 ｛ｕ（ｒ）：ｒ≥ｔ｝∩Ｆ（ｓ）的唯一点。

Let X be a uniformly convex Banach space with a Fr chet differentiable norm, C be a bounded closed convex subset of X, and S = {T(t): t≥0} be an aspoptoticajly nonexpansive semigroup on C. If u(·): [0, ∞) → C is an almost-orbit of S which is uniformly continuous in t ∈[0, ∞) then {u(t): t≥0} almost converges weakly to the unique point of the set,.