Balls in the triangular ratio metric
  We consider the triangular ratio metric and estimate the radius of convexity for balls in some special domains and prove the inclusion relations of metric balls defined by the triangular ratio metric, the quasihyperbolic metric and the $j$-metric. 
Sami Hokuni, Riku Kl\'en, Yaxiang Li, Matti Vuorinen
math.MG