Rough Statistical Convergence of Double Sequences in Probabilistic Normed Spaces

TL;DR

This paper introduces generalized notions of rough statistical convergence and cluster points for double sequences in probabilistic normed spaces, expanding existing concepts in normed linear spaces and exploring their properties.

Contribution

It defines rough statistical convergence and cluster points in probabilistic normed spaces, and establishes key relations between limits and cluster points for double sequences.

Findings

Defined rough statistical convergence in probabilistic normed spaces

Proved relations between rough statistical limits and cluster points

Extended convergence concepts from normed to probabilistic spaces

Abstract

In this paper, we have defined rough convergence and rough statistical convergence of double sequences in probabilistic normed spaces which is more generalized version than the rough statistical convergence of double sequences in normed linear spaces. Also, we have defined rough statistical cluster points of double sequences and then, investigated some important results associated with the set of rough statistical limits of double sequences in these spaces. Moreover, in the same spaces, we have proved an important relation between the set of all rough statistical cluster points and rough statistical limits under certain condition.