正级数的收敛性与理想收敛性

IF 0.3 Q4 MATHEMATICS

Annales Mathematicae et Informaticae Pub Date : 2020-01-01 DOI:10.33039/ami.2020.05.005

V. Baláž, Kálmán Liptai, János Tóth T., T. Visnyai

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引用次数: 0

摘要

让ℐ⊆2 N是一个容许理想,我们说一个序列(𝑥𝑛)的实数ℐ−𝐿收敛于一个数字,和写ℐ−lim𝑥𝑛=𝐿,如果每个𝜀> 0集𝐴𝜀={𝑛:|𝑥𝑛−𝐿|≥𝜀}属于理想ℐ。讨论了正级数的收敛性与和数列的收敛性之间的关系。具体来说，我们研究了具有以下性质的理想:

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Convergence of positive series and ideal convergence

Let ℐ ⊆ 2 N be an admissible ideal, we say that a sequence ( 𝑥 𝑛 ) of real numbers ℐ− converges to a number 𝐿 , and write ℐ − lim 𝑥 𝑛 = 𝐿 , if for each 𝜀 > 0 the set 𝐴 𝜀 = { 𝑛 : | 𝑥 𝑛 − 𝐿 | ≥ 𝜀 } belongs to the ideal ℐ . In this paper we discuss the relation ship between convergence of positive series and the convergence properties of the summand sequence. Concretely, we study the ideals ℐ having the following property as well:

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来源期刊

Annales Mathematicae et Informaticae MATHEMATICS-

CiteScore

0.90

自引率

0.00%

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