On the average scale-invariant Cassinian metric

TL;DR

This paper explores the properties of the average scale-invariant Cassinian metric, relating it to other hyperbolic metrics and examining the convexity of metric balls in punctured Euclidean spaces.

Contribution

It establishes geometric relationships between the average scale-invariant Cassinian metric and hyperbolic metrics, and analyzes convexity properties of metric balls.

Findings

Established relationships with hyperbolic metrics

Analyzed local convexity of metric balls

Provided geometric insights into the scale-invariant Cassinian metric

Abstract

We establish geometric relationships between the average scale-invariant Cassinian metric and other hyperbolic type metrics. In addition, we study the local convexity properties of the scale-invariant metric balls in Euclidean once punctured spaces.