Rough convergence of sequences in a cone metric space

TL;DR

This paper introduces the concept of rough convergence for sequences within cone metric spaces and explores how basic properties from normed linear spaces translate to this new setting.

Contribution

It presents the first study of rough convergence in cone metric spaces and examines the extent to which properties from normed spaces are preserved.

Findings

Established the definition of rough convergence in cone metric spaces.

Analyzed the impact of cone metric structure on classical convergence properties.

Identified which properties of rough convergence carry over from normed spaces.

Abstract

Here we have introduced the idea of rough convergence of sequences in a cone metric space. Also it has been investigated how far several basic properties of rough convergence as valid in a normed linear space are affected in a cone metric space.