New Results in Gradual Normed Linear Spaces in Light of Generalized Statistical Convergence via Ideal

Abstract

This article introduces the novel concept of rough $\mathcal{I}-$statistical
convergence in gradual normed linear spaces (GNLS). The paper presents noteworthy findings utilizing the $\mathcal{I}_{st}^{r,\alpha}(\mathcal{G})-$
limit set, which exhibits several fundamental properties of the concept. Moreover, a necessary and sufficient condition for $\mathcal{I}_{st}^{r,\alpha}\mathcal{G})-$convergence of a sequence in a GNLS is established.