Abstract

In this article, we introduce the notion of $\mathcal{I}$-statistical convergence of sequences as one of the extensions of $\mathcal{I}$-convergence in the gradual normed linear spaces. We investigate some fundamental properties of the newly introduced notion and its relation with some other methods of convergence. Also we introduce and investigate the concept of $\mathcal{I}$-statistical limit points, cluster points and establish some implication relations.

Keywords: Gradual number; gradual normed linear spaces; statistical convergence; $\mathcal{I}$-convergence; $\mathcal{I}$-statistical convergence.

MSC: 03E72, 40A35, 40A05

Pages:  218$-$228     

Volume  74 ,  Issue  3 ,  2022