On statistical A $\mathfrak{A}$ -Cauchy and statistical A $\mathfrak{A}$ -summability via ideal

Journal of Inequalities and Applications

M. Mursaleen¹  Osama H. H. Edely² 

[1] Department of Mathematics, Aligarh Muslim University;Department of Mathematics, Tafila Technical University;

关键词: Statistical A I $\mathfrak{A}^{\mathfrak{I}}$ -limit superior;    Statistical A I $\mathfrak{A}^{\mathfrak{I}}$ -limit inferior;    Statistical A I $\mathfrak{A}^{\mathfrak{I}}$ -bounded;    Statistical A I $\mathfrak{A}^{\mathfrak{I}}$ -Cauchy summability;    Statistical A I ∗ $\mathfrak{A}^{\mathfrak{I}^{\ast }}$ -Cauchy summability;    Tauberian theorem;   

DOI  :  10.1186/s13660-021-02564-4

来源: DOAJ

【 摘 要 】

Abstract The notion of statistical convergence was extended to I $\mathfrak{I}$ -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 A I $\mathfrak{A}^{\mathfrak{I}}$ -Cauchy and statistically A I ∗ $\mathfrak{A}^{\mathfrak{I}^{\ast }}$ -Cauchy summability via the notion of ideal. We obtain some relations between them and prove that under certain conditions statistical A I $\mathfrak{A}^{\mathfrak{I}}$ -Cauchy and statistical A I ∗ $\mathfrak{A}^{\mathfrak{I}^{\ast }}$ -Cauchy summability are equivalent. Moreover, we give some Tauberian theorems for statistical A I $\mathfrak{A}^{\mathfrak{I}}$ -summability.

【 授权许可】

Unknown