ON $\mathcal{I}$-CAUCHY SEQUENCES
Copyright policy )ON $\mathcal{I}$-CAUCHY SEQUENCES
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.
40A05, ideals of sets, 46A99, $\mathcal{I}^*$-Cauchy, $\mathcal{I}$-convergence, statistical convergence, $\mathcal{I}$-Cauchy, 40A99, statistical Cauchy sequence
40A05, ideals of sets, 46A99, $\mathcal{I}^*$-Cauchy, $\mathcal{I}$-convergence, statistical convergence, $\mathcal{I}$-Cauchy, 40A99, statistical Cauchy sequence
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