ON $\mathcal{I}$-CAUCHY SEQUENCES

Abstract

The concept of $\mathcal{I}$-convergence is a generalization of statistical convergence and it is dependent on the notion of the ideal $\mathcal{I}$ of subsets of the set $\mathbb{N}$ of positive integers. In this paper we prove a decomposition theorem for $\mathcal{I}$-convergent sequences and we introduce the notions of $\mathcal{I}$ Cauchy sequence and $\mathcal{I}^{*}$-Cauchy sequence, and then study their certain properties.