Statistical and rough statistical convergence in an S-metric space

TL;DR

This paper introduces and studies statistical and rough statistical convergence in S-metric spaces, exploring their properties, related concepts like Cauchyness and boundedness, and the set of limit points.

Contribution

It extends the concepts of statistical convergence to S-metric spaces and investigates their fundamental properties and related notions.

Findings

Defined statistical and rough statistical convergence in S-metric spaces

Established properties of these convergence types

Analyzed the set of rough statistical limit points

Abstract

In this paper, using the concept of natural density, we have introduced the ideas of statistical and rough statistical convergence in an $S$-metric space. We have investigated some of their basic properties. We have defined statistical Cauchyness and statistical boundedness of sequences and then some results related these ideas have been studied. We have defined the set of rough statistical limit points of a sequence in an $S$-metric space and have proved some relevant results associated with such type of convergence