【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u(·):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.更多还原

【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.更多还原