# Rough $I$-convergence in cone metric spaces

## TL;DR

This paper introduces and explores the concepts of rough $I$-convergence and rough $I^*$-convergence in cone metric spaces, extending existing ideas of convergence using ideals.

## Contribution

It defines rough $I$-convergence and rough $I^*$-convergence in cone metric spaces and investigates their relationship, advancing the theoretical framework of convergence in these spaces.

## Key findings

- Defined rough $I$-convergence in cone metric spaces.
- Introduced rough $I^*$-convergence and analyzed its relation to rough $I$-convergence.
- Established theoretical properties connecting the two types of convergence.

## Abstract

Here we have studied the notion of rough $I$-convergence as an extension of the idea of rough convergence in a cone metric space using ideals. We have further introduced the notion of rough $I^*$-convergence of sequences in a cone metric space to find the relationship between rough $I$ and $I^*$-convergence of sequences.