Convexity properties of quasihyperbolic balls on Banach spaces

TL;DR

This paper investigates the convexity and starlikeness of quasihyperbolic and distance ratio metric balls within Banach spaces, focusing on convex domains and punctured spaces to understand their geometric properties.

Contribution

It provides new insights into the convexity properties of these metric balls on Banach spaces, especially in convex and punctured domains.

Findings

Convexity properties of quasihyperbolic balls are characterized in Banach spaces.

Starlikeness of metric balls is analyzed in various domain configurations.

Results extend understanding of geometric structures in infinite-dimensional spaces.

Abstract

We study convexity and starlikeness of quasihyperbolic and distance ratio metric balls on Banach spaces. In particular, problems related to these metrics on convex domains, and on punctured Banach spaces, are considered.