Strong $I$ AND $I^{\ast }$-statistically pre-Cauchy double sequences in Probabilistic Metric Spaces

Abstract

In this paper we consider the notion of strong $I$-statistically pre-Cauchy double sequences in probabilistic metric spaces in line of Das et. al. [6] and introduce the new concept of strong $I^{\ast }$-statistically pre-Cauchy double sequences in real line as well as in probabilistic metric spaces. We mainly study inter relationship among strong $I$-statistical convergence, strong $I$-statistical pre-Cauchy condition and strong $I^{\ast }$-statistical pre-Cauchy condition for double sequences in probabilistic metric spaces and examine some basic properties of these notions.