Growth of Some Hyperbolic Type Distances and Starlikeness of Metric Balls

The purpose of this paper is to study geometric properties of some hyperbolic type metrics, including the growth of distances along Euclidean line segments, bounds of metrics, and the starlikeness and convexity of metric balls.

Automated summary

The purpose of this paper is to investigate the geometric properties of certain hyperbolic type metrics, such as the increase in distances along Euclidean line segments, metric bounds, and the starlikeness and convexity of metric balls.