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

Abstract

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