Arzela Ascoli Theorem in Quasi Cone Metric Space

TL;DR

This paper extends the Arzela Ascoli Theorem to quasi cone metric spaces, introducing new concepts like forward and backward equicontinuity and exploring their implications using various topologies.

Contribution

It generalizes classical results to quasi cone metric spaces and introduces the novel notions of forward and backward equicontinuity.

Findings

Established Arzela Ascoli Theorem in quasi cone metric spaces

Introduced forward and backward equicontinuity concepts

Analyzed properties using forward and backward topologies

Abstract

In this paper we investigate Arzela Ascoli Theorem in quasi cone metric space, which is a generalization of metric space. We prove some interesting results using forward and backward toplologies, forward and backward continuity and forward and backward totally boundedness. A new notion forward and backward equicontinuity is also introduced.