Journal of Prime Research in Mathematics

# On the power mean inequality of the hyperbolic metric of unit ball

Barkat Ali Bhayo
Department of Mathematics & Statistics, Quaid-e-Awam University of Engineering Science & Technology, Nawabshah, Pakistan.

$$^{1}$$Corresponding Author: bhayo.barkat@gmail.com

### Abstract

The hyperbolic distances from the origin are changed under the radial selfmapping $$x → |x|^{1/K−1}x$$, $$K > 1$$ of the unit ball. Here author gives the power mean inequality of the hyperbolic metric under the radial mapping.

#### Keywords:

Power Mean, inequalities, hyperbolic metric, distortion function.