Arithmetic continuity in quasi cone metric spaces

TL;DR

This paper introduces new types of continuity and compactness in quasi cone metric spaces based on arithmetic convergence, providing new insights into their structural properties.

Contribution

It defines arithmetic ff-continuity and fb-continuity, and establishes forward and backward arithmetic compactness in quasi cone metric spaces, advancing the theoretical framework.

Findings

Introduction of arithmetic ff-continuity and fb-continuity

Establishment of forward and backward arithmetic compactness

Proved related theorems using these new concepts

Abstract

In this paper we have introduced arithmetic ff-continuity and arithmetic fb-continuity utilizing the concept of forward and backward arithmetic convergence in quasi cone metric spaces. These concepts are used to prove some fascinating results. The notions of forward and backward arithmetic compactness in quasi cone metric spaces are also established which are further utilized to prove some related results.