Abstract
In [Analysis 1985, 5 (4), 301-313], J.A. Fridy proved an equivalence relation between statistical convergence and statistical Cauchy sequence. In this paper, we define AI*-statistical convergence and find under certain conditions, that it is equivalent to AI-statistical convergence defined in [Appl. Math. Lett. 2012, 25 (4), 733-738]. Moreover, we define AI- and AI*-statistical Cauchy sequences and find some equivalent relation with AI- and AI*-statistical convergence.