TVS-锥度量空间中的统计收敛

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TVS-锥度量空间中的统计收敛林艳芳, 鲍玲鑫福建农林大学计算机与信息学院福州 350002 Statistical Convergence in TVS-cone Metric Spaces Yan Fang LIN, Ling Xin BAOSchool of Computer and Information, Fujian Agriculture and Forestry University, Fuzhou 350002, P. R. China

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摘要本文研究TVS-锥度量空间中的统计收敛以及TVS-锥度量空间的统计完备性.令（X，E，P，d）表示一个TVS-锥度量空间.利用定义在有序Hausdorff拓扑向量空间E上的Minkowski函数ρ，证明了在X上存在一个通常意义下的度量d_ρ，使得X中的序列（x_n）在锥度量d意义下统计收敛到x ∈ X，当且仅当（x_n）在度量d_ρ意义下统计收敛到x.基于此，我们证明了任意一个TVS-锥统计Cauchy序列是几乎处处TVS-锥Cauchy序列，还证明了任意一个TVS-锥统计收敛的序列是几乎处处TVS-锥收敛的.从而，TVS-锥度量空间（X，d）是d-完备的，当且仅当它是d-统计完备的.基于以上结论，通常度量空间中统计收敛的许多性质都可以平行地推广到锥度量空间中统计收敛的情形.

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收稿日期: 2019-11-27

MR (2010):

O177

基金资助:国家自然科学基金资助项目（11501108）；福建省自然科学基金资助项目（2019J01400）；福建农林大学****计划项目（2016011）

通讯作者:鲍玲鑫E-mail: bolingxmu@sina.com

作者简介: 林艳芳,E-mail:yanfang_lin@foxmail.com

引用本文:

林艳芳, 鲍玲鑫. TVS-锥度量空间中的统计收敛[J]. 数学学报, 2020, 63(5): 523-530. Yan Fang LIN, Ling Xin BAO. Statistical Convergence in TVS-cone Metric Spaces. Acta Mathematica Sinica, Chinese Series, 2020, 63(5): 523-530.

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