On strong ${\mathcal{A}}^{\mathcal{I}}$-statistical convergence of sequences in probabilistic metric spaces

Abstract

In this paper using a non-negative regular summability matrix $\mathcal{A}$ and a non-trivial admissible ideal $\mathcal{I}$ in $\mathbb{N}$ we study some basic properties of strong ${\mathcal{A}}^{\mathcal{I}}$-statistical convergence and strong ${\mathcal{A}}^{\mathcal{I}}$-statistical Cauchyness of sequences in probabilistic metric spaces not done earlier. We also introduce strong ${\mathcal{A}}^{{\mathcal{I}}^{\ast }}$-statistical Cauchyness in probabilistic metric space and study its relationship with strong A${\mathcal{A}}^{\mathcal{I}}$-statistical Cauchyness there. Further, we study some basic properties of strong ${\mathcal{A}}^{\mathcal{I}}$-statistical limit points and strong ${\mathcal{A}}^{\mathcal{I}}$-statistical cluster points of a sequence in probabilistic metric spaces.

arXiv admin note: substantial text overlap with arXiv:2204.02727, arXiv:2007.09173