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

Abstract The 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 statistically $\mathfrak{A}^{\mathfrak{I}}$ A -Cauchy $\mathfrak{A}^{\mathfrak{I}^{\ast }}$ ∗ summability via ideal. We obtain some relations between them prove that under certain conditions are equivalent. Moreover, give Tauberian theorems for -summability.