Comparison theorems for hyperbolic type metrics

TL;DR

This paper explores relationships between various hyperbolic type metrics in Euclidean subdomains, introducing a new metric and comparing it to the existing distance ratio metric to understand their connections.

Contribution

A new hyperbolic type metric is introduced and systematically compared to the distance ratio metric in Euclidean subdomains.

Findings

The new metric exhibits specific properties relative to existing metrics.

Comparative analysis reveals conditions under which metrics are equivalent or dominate each other.

The study enhances understanding of hyperbolic metrics in geometric function theory.

Abstract

The connection between several hyperbolic type metrics is studied in subdomains of the Euclidean space. In particular, a new metric is introduced and compared to the distance ratio metric.