# Arithmetic continuity in cone metric space

by Taja Yaying

Received on:18.05.2020 | Revised on:10.10.2020 | Accepted on: 19.10.2020

Abstract:

William Henry Ruckle introduced the notion of arithmetic convergence in the sense that a sequence  defined on the set of natural numbers  is said to be arithmetic convergent if for each  there is an integer  such that for every integer , , where  denotes the greatest common divisor of m and n. In this paper, the notion of arithmetic convergence has been extended to cone metric space. Using the concept of arithmetic convergence, arithmetic continuity and arithmetic compactness have been defined in cone metric spaces and give some interesting results.

Cite as:

Yaying T. 2020. On Arithmetic Continuity in Cone Metric Space, Dera Natung Government College Research Journal, 5, 55-62.