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The concept of I-convergence is a generalization of statistical convergence and it is dependent on the notion of the ideal I of subsets of the set N of positive integers. In this paper we prove a decomposition theorem for I-convergent sequences and we introduce the notions of I Cauchy sequence and I*-Cauchy sequence, and then study their certain properties.
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Nabiev et al. (2007) studied this question.
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