On strong {\lambda}-statistical convergence of sequences in probabilistic metric (pm) spaces

TL;DR

This paper investigates the properties of strong lambda-statistical convergence and related concepts like Cauchyness, limit points, and cluster points in probabilistic metric spaces, expanding the theoretical framework of convergence in such spaces.

Contribution

It introduces and analyzes the notions of strong lambda-statistical Cauchyness, limit points, and cluster points in probabilistic metric spaces, establishing their interrelationships.

Findings

Established properties of strong lambda-statistical convergence.

Defined and explored strong lambda-statistically Cauchy sequences.

Analyzed relationships among limit points and cluster points.

Abstract

In this paper we study some basic properties of strong {\lambda}- statistical convergence of sequences in probabilistic metric (PM) spaces. We also introduce and study the notion of strong {\lambda}-statistically Cauchyness. Further introducing the notions of strong {\lambda}-statistical limit point and strong {\lambda}-statistical cluster point of a sequence in a probabilistic metric (PM) space we examine their interrelationship.