Inclusion relations of hyperbolic type metric balls II

TL;DR

This paper investigates the inclusion relations among metric balls defined by hyperbolic, quasihyperbolic, j-metric, and chordal metrics within the unit ball, enhancing understanding of their geometric interactions.

Contribution

It provides new insights into the inclusion relations of various hyperbolic-type metric balls in the unit ball, extending previous studies to multiple metrics.

Findings

Established inclusion relations among hyperbolic, quasihyperbolic, and j-metric balls.

Compared the geometric properties of these metric balls within the unit ball.

Extended known results to include the chordal metric.

Abstract

Inclusion relations of metric balls defined by the hyperbolic, the quasihyperbolic, the $j$-metric and the chordal metric will be studied. The hyperbolic metric, the quasihyperbolic metric and the $j$-metric are considered in the unit ball.