Rough $\mathcal{I}$-convergence of sequences in probabilistic normed spaces

Abstract

In this paper, we have studied the idea of rough $\mathcal{I}$-convergence in probabilistic normed spaces which is indeed a generalized version as compared to the notion of rough $\mathcal{I}$-convergence in normed linear spaces. On the other way, it is also a generalization of rough statistical convergence in probabilistic normed spaces. Furthermore, we have defined the notion of rough $\mathcal{I}$-cluster points and have proved some important results associated with the set of rough $\mathcal{I}$-limits of a sequence in the same space.