A study on strong AI-statistical convergence of sequences in probabilistic metric spaces

Abstract

In this paper using a non-negative regular summability matrix A and a non-trivial admissible ideal I in N we study some basic properties of strong AI-statistical convergence and strong AI-statistical Cauchyness of sequences in probabilistic metric spaces not done earlier. We also introduce the notion of strong AI∗-statistical Cauchyness and study its relationship with strong AI-statistical Cauchyness. Further we study some basic properties of strong AI-statistical limit points and strong AI-statistical cluster points of a sequence in probabilistic metric spaces.