Rough $\mathcal{I}$-statistical convergence in a partial metric space

TL;DR

This paper introduces and studies rough $\\mathcal{I}$-statistical convergence in partial metric spaces, extending existing concepts of rough statistical and rough ideal convergence, and explores properties of the associated limit sets.

Contribution

It presents a new convergence concept in partial metric spaces, combining rough, statistical, and ideal convergence notions, and analyzes its properties.

Findings

Defined rough $\\mathcal{I}$-statistical limit set.

Established properties of the limit set.

Extended convergence theories in partial metric spaces.

Abstract

In this paper we study the notion of rough $\mathcal{I}$-statistical convergence of sequences in a partial metric space as an extension work of both the notions of rough statistical and rough ideal convergence. Here we define rough $\mathcal{I}$-statistical limit set and discuss some relevant properties associated with this set.