# [1]沈虹,何建敏,凡震彬.Opial条件下渐近非扩张型半群殆轨道的遍历定理[J].东南大学学报(自然科学版),2009,39(6):1283-1286.[doi:10.3969/j.issn.1001-0505.2009.06.038] 　Shen Hong,He Jianmin,Fan Zhenbin.Ergodic theorem of almost-orbits for asympotically nonexpansive type semigroups under Opial condition[J].Journal of Southeast University (Natural Science Edition),2009,39(6):1283-1286.[doi:10.3969/j.issn.1001-0505.2009.06.038] 点击复制 Opial条件下渐近非扩张型半群殆轨道的遍历定理() 分享到： var jiathis_config = { data_track_clickback: true };

39

2009年第6期

1283-1286

2009-11-20

## 文章信息/Info

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

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
Author(s):
1 School of Economics and Management, Southeast University, Nanjing 210096, China
2 Changshu Institute of Technology, Changshu 215500, China

Keywords:

O177.91
DOI:
10.3969/j.issn.1001-0505.2009.06.038

X是一Banach空间,(X,τ)是局部凸线性拓扑空间,CX上的τ-序列紧凸集,SC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.
Abstract:
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.

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