Rough I-statistical convergence of sequences

TL;DR

This paper introduces the concept of rough I-statistical convergence in normed linear spaces, expanding the framework of I-statistical convergence by incorporating rough limits and exploring their topological properties.

Contribution

It extends the existing notion of I-statistical convergence to include rough limits and analyzes their topological characteristics in normed linear spaces.

Findings

Defined the set of rough I-statistical limits of a sequence.

Explored topological properties of the set of rough I-statistical limits.

Extended the theory of I-statistical convergence with roughness concepts.

Abstract

The concept of I-statistical convergence of sequence was first defined by Das et.al [2]. In this paper we introduce and study the notion of rough I-statistical convergence of sequence in normed linear Spaces. We also define the set of rough I-statistical limits of a sequence and discuss some topological properties of this set.