| Hilbert空间中渐近殆非扩张曲线的强遍历收敛定理 |
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| 引用本文： | 董琪翔,李刚.Hilbert空间中渐近殆非扩张曲线的强遍历收敛定理[J].应用泛函分析学报,2008,10(2):100-108. |
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| 作者姓名： | 董琪翔 李刚 |
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| 作者单位： | 扬州大学数学科学学院,江苏扬州225002 |
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| 摘 要： | 设C为Hilbert空间H的非空子集，G为一个交换半群．文中定义了G上渐近殆非扩张曲线“（·）：G→C，证明了渐近殆非扩张曲线的强遍历收敛定理．应用于半群，得到了在失去凸性的情况下，渐近非扩张型半群的殆轨道的强遍历收敛定理．推广和改进了以前所有的结果。
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| 关 键 词： | 渐近殆非扩张 非线性算子半群 遍历定理 |
Strong Ergodic Theorem for Asymptotically Almost Non-expansive Curves in Hilbert Spaces |
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| DONG Qi-xiang,LI Gang.Strong Ergodic Theorem for Asymptotically Almost Non-expansive Curves in Hilbert Spaces[J].Acta Analysis Functionalis Applicata,2008,10(2):100-108. |
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| Authors: | DONG Qi-xiang LI Gang |
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| Institution: | ( School of Mathematical Science, Yangzhou University, Yangzhou Jiangsu 225002, China) |
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| Abstract: | Let C be a nonempty subset of a Hilbert space H, and G a commutative semi-topological semigroup. We first give the definition of asymptotically almost non-expansive curve u(·):G→C. Then we prove the strong ergodic theorem for asymptotically almost non-expansive curves. As applications, we obtain the strong ergodic theorem for the almost orbits of asymptotically non- expansive type semigroups without convexity, which extends and improves all the previous results. |
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| Keywords: | asymptotically almost non-expansive ergodic theorem |
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