| 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 |
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| 引用本文： | 曾六川.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[J].数学学报,1996,39(6):796-802. |
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| 作者姓名： | 曾六川 |
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| 作者单位： | 上海师范大学数学系 |
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| 摘 要： | 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。
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| 关 键 词： | 几乎轨道，渐近非扩张半群，遍历定理，不动点 |
| 收稿时间： | 1993-12-3 |
| 修稿时间： | 1995-3-17 |
On the Asymptotic Behavior of Almost-orbits of Asymptotically Nonexpansive Semigroups in Uniformly Convex Banach Spaces |
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| Zeng Luchuan.On the Asymptotic Behavior of Almost-orbits of Asymptotically Nonexpansive Semigroups in Uniformly Convex Banach Spaces[J].Acta Mathematica Sinica,1996,39(6):796-802. |
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| Authors: | Zeng Luchuan |
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| Institution: | Zeng Luchuan(Shanghai Normal University,Shanghai 200234,China) |
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| Abstract: | 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,. |
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| Keywords: | Almost-orbit Asymptotically nonexpansive semigroup Ergodic theorem Fixedpoint |
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