Opial条件下渐近非扩张型半群殆轨道的遍历定理  

Ergodic theorem of almost-orbits for asympotically nonexpansive type semigroups under Opial condition

作　　者：沈虹[1] 何建敏[1] 凡震彬[2] 

机构地区：[1]东南大学经济管理学院,南京210096 [2]常熟理工学院数学系,常熟215500

出　　处：《东南大学学报（自然科学版）》2009年第6期1283-1286,共4页Journal of Southeast University：Natural Science Edition

摘　　要：X是一Banach空间,(X,τ)是局部凸线性拓扑空间,C是X上的τ-序列紧凸集,S是C上的Γ类渐近非扩张型半群.首先给出了局部一致τ-Opial条件的概念,运用乘积拓扑网技巧得到了具有局部一致τ-Opial条件下空间X的新的收敛条件.然后利用该收敛条件得到了在局部一致τ-Opial条件下的Γ类渐近非扩张型半群殆轨道的遍历定理以及τ-收敛定理.结论是将已有结果由一致τ-Opial条件推广到局部一致τ-Opial条件,对空间X的要求进一步减弱,该结论是遍历定理在非一致凸空间中的延伸.Let X be a Banach space,（X,τ） be a locally convex linear topological space,C is a τ-sequence compact convex subset of X,and S an asymptotically nonexpansive type semigroups from C onto itself.Under the locally uniform τ-Opial condition,using product topological net,a new convergence condition of X with locally uniform τ-Opial condition is obtained, and give the ergodic theorem and τ-convergence theorem of the almost-orbits for asympotically nonexpansive typesemigroups in Banach space X are given.The conclusion generalizes the previous results under the locally uniform τ-Opial condition,and further weakens the demand of space X.These results are an extension and breakthrough of ergodic theorems in non uniform convex spaces.

关 键 词：BANACH空间 渐近非扩张型半群 τ-收敛 遍历定理 

分 类 号：O177.91[理学—数学]