Rough convergence of sequences in a partial metric space

TL;DR

This paper explores the concept of rough convergence of sequences within partial metric spaces, examining how classical results from metric spaces adapt or change in this broader context.

Contribution

It introduces the notion of rough convergence in partial metric spaces and investigates the impact on boundedness and limit sets, extending existing metric space results.

Findings

Rough convergence is well-defined in partial metric spaces.

Classical properties of boundedness are affected in partial metric spaces.

Results on rough limit sets are generalized to partial metric spaces.

Abstract

In this paper we have studied the notion of rough convergence of sequences in a partial metric space. We have also investigated how far several relevant results on boundedness, rough limit sets etc. which are valid in a metric space are affected in a partial metric space.