Strong $I$ AND $I^*$-statistically pre-Cauchy double sequences in Probabilistic Metric Spaces

TL;DR

This paper introduces and studies new types of pre-Cauchy double sequences in probabilistic metric spaces, focusing on strong $I$- and $I^*$-statistical properties and their interrelationships.

Contribution

It proposes the concepts of strong $I^*$-statistically pre-Cauchy double sequences and explores their connections with existing convergence and pre-Cauchy notions in probabilistic metric spaces.

Findings

Established relationships among strong $I$-statistical convergence, pre-Cauchy, and $I^*$-pre-Cauchy conditions.

Defined new classes of sequences in probabilistic metric spaces.

Analyzed basic properties of these sequence classes.

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 $I^*$-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 $I^*$-statistical pre-Cauchy condition for double sequences in probabilistic metric spaces and examine some basic properties of these notions.