| 部分和有界的级数在Cesaro意义下收敛性的条件 |
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| 引用本文： | 欧阳露莎,刘敏思. 部分和有界的级数在Cesaro意义下收敛性的条件[J]. 中南民族大学学报(自然科学版), 2012, 31(1): 114-116 |
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| 作者姓名： | 欧阳露莎 刘敏思 |
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| 作者单位： | 1. 中南民族大学数学与统计学学院,武汉,430074
2. 华中师范大学数学与统计学学院,武汉,430079 |
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| 基金项目： | 国家自然科学基金资助项目(60904005);教育部财政部2010年度国家级教学团队“数学与应用数学专业主干课程”建设项目(教高函【2010】12号);中南民族大学自然科学基金资助项目(JYX11036) |
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| 摘 要： | 将级数在Cesaro意义下的收敛性转化为适当数列的均值收敛问题,巧妙构造一个有界数列得到了有界数列均值收敛性的一般性结论,再通过建立数列的有限权重分解,得到了关于有界数列均值收敛的一些有益的结论,进而更完整地解决了级数在Cesaro意义下收敛性的条件问题.
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| 关 键 词： | Cesaro意义下收敛 均值收敛 权重 有限权重分解 |
Convergence Condition of Series with Finite Partial Sums under Cesaro |
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| Ouyang Lusha,Liu Minsi. Convergence Condition of Series with Finite Partial Sums under Cesaro[J]. Journal of South-Central Univ for, 2012, 31(1): 114-116 |
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| Authors: | Ouyang Lusha Liu Minsi |
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| Affiliation: | 1 College of Mathematics and Statistics,South-Central University for Nationalitics,Wuhan 430074,China; 2 College of Mathematics and Statistics,Central China Normal University,Wuhan 430079,China) |
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| Abstract: | In this paper,we change the series convergence under Cesaro into the mean convergence of a appropriate sequence of number.Through constructing a bounded sequence of number skillfully,we get the general conclusion of the mean convergence of bounded sequence of number.Furthermore,we give the finite weight decomposition of sequence of number by introducing the weight of subsequence,and derive some useful results about the mean convergence of bounded sequence of number.With all above discussions,we resolve the series convergence under Cesaro completely. |
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| Keywords: | convergence under Cesaro mean convergence weight finite weight decomposition |
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