Abstract
In this paper, we introduce the concepts of $\mathcal{I}$ and $\mathcal{I^{*}}-$convergence of sequences in gradual normed linear spaces. We study some basic properties and implication relations of the newly defined convergence concepts. Also, we introduce the notions of $\mathcal{I}$ and $\mathcal{I^{*}}-$Cauchy sequences in the gradual normed linear space and investigate the relations between them.
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