Rough ideal convergence in a partial metric space

TL;DR

This paper extends the concept of rough convergence in partial metric spaces by incorporating ideals, defining new limit and cluster point sets, and establishing related properties.

Contribution

It introduces the notion of rough ideal convergence in partial metric spaces, expanding the theoretical framework of convergence concepts.

Findings

Defined rough $\\mathcal{I}$-limit points and cluster points

Proved properties of these new sets

Extended rough convergence theory in partial metric spaces

Abstract

In this paper, using the concept of ideal, we study the idea of rough ideal convergence of sequences which is an extension of the notion of rough convergence of sequences in a partial metric space. We define the set of rough $\mathcal{I}$-limit points and the set of rough $\mathcal{I}$-cluster points and then we prove some relevant results associated with these sets.