\(\mathcal{I}_2\)-Cauchy double sequences in 2-normed spaces

Abstract

The concept \(\mathcal{I}\)-Cauchy and \(\mathcal{I}^{*}\)-Cauchy sequences were studied by Gudal and Acik in on \(\mathcal{I}\)-Cauchy sequences in 2-normed spaces, Math. Inequal. Appl. 11 (2) (2008), 349--354. In this paper, we introduce the notions of \(\mathcal{I}_2\)-Cauchy and \(\mathcal{I}_2^{*}\)-Cauchy double sequences, and study their some properties with (AP2) in 2-normed spaces.