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On statistical \(\mathfrak{A}\)-Cauchy and statistical \(\mathfrak{A}\)-summability via ideal
Journal of Inequalities and Applications ( IF 1.5 ) Pub Date : 2021-02-17 , DOI: 10.1186/s13660-021-02564-4
Osama H. H. Edely , M. Mursaleen

The notion of statistical convergence was extended to $\mathfrak{I}$ -convergence by (Kostyrko et al. in Real Anal. Exch. 26(2):669–686, 2000). In this paper we use such technique and introduce the notion of statistically $\mathfrak{A}^{\mathfrak{I}}$ -Cauchy and statistically $\mathfrak{A}^{\mathfrak{I}^{\ast }}$ -Cauchy summability via the notion of ideal. We obtain some relations between them and prove that under certain conditions statistical $\mathfrak{A}^{\mathfrak{I}}$ -Cauchy and statistical $\mathfrak{A}^{\mathfrak{I}^{\ast }}$ -Cauchy summability are equivalent. Moreover, we give some Tauberian theorems for statistical $\mathfrak{A}^{\mathfrak{I}}$ -summability.

中文翻译:

关于统计\(\ mathfrak {A} \)-求和和统计\(\ mathfrak {A} \) -通过理想求和

(Kostyrko et al。in Real Anal。Exch。26(2):669–686,2000)将统计收敛的概念扩展到$ \ mathfrak {I} $ -convergence。在本文中,我们使用了这种技术,并介绍了统计上的$ \ mathfrak {A} ^ {\ mathfrak {I}} $-漂亮和统计上$ \ mathfrak {A} ^ {\ mathfrak {I} ^ {\ ast}的概念} $-通过“理想”的概念来实现可求和。我们获得它们之间的一些关系,并证明在某些条件下,统计$ \ mathfrak {A} ^ {\ mathfrak {I}} $-漂亮,而统计$ \ mathfrak {A} ^ {\ mathfrak {I} ^ {\ ast} } $-漂亮的可加性是等效的。此外,我们给出了统计$ \ mathfrak {A} ^ {\ mathfrak {I}} $-可和性的一些Tauberian定理。
更新日期:2021-02-17
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