中南民族大学学报：自然科学版
中南民族大學學報：自然科學版
중남민족대학학보：자연과학판
Journal of South-Central University for Nationalities
2012年
1期
114-116
,共3页
Cesaro意义下收敛%均值收敛%权重%有限权重分解
Cesaro意義下收斂%均值收斂%權重%有限權重分解
Cesaro의의하수렴%균치수렴%권중%유한권중분해
convergence under Cesaro%mean convergence%weight%finite weight decomposition
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.
將級數在Cesaro意義下的收斂性轉化為適噹數列的均值收斂問題,巧妙構造一箇有界數列得到瞭有界數列均值收斂性的一般性結論,再通過建立數列的有限權重分解,得到瞭關于有界數列均值收斂的一些有益的結論,進而更完整地解決瞭級數在Cesaro意義下收斂性的條件問題.
장급수재Cesaro의의하적수렴성전화위괄당수렬적균치수렴문제,교묘구조일개유계수렬득도료유계수렬균치수렴성적일반성결론,재통과건립수렬적유한권중분해,득도료관우유계수렬균치수렴적일사유익적결론,진이경완정지해결료급수재Cesaro의의하수렴성적조건문제.
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.
