Inclusion Properties of the Triangular Ratio Metric Balls

Abstract

<p> Inclusion properties are studied for balls of the triangular ratio metric, the hyperbolic metric, the j∗-metric, and the distance ratio metric defined in the unit ball domain. Several sharp results are proven and a conjecture about the relation between triangular ratio metric balls and hyperbolic balls is given. An algorithm is also built for drawing triangular ratio circles or three-dimensional spheres.<br></p>