Journal of Prime Research in Mathematics
Vol. 1 (2012), Issue 1, pp. 45 – 50
ISSN: 1817-3462 (Online) 1818-5495 (Print)
ISSN: 1817-3462 (Online) 1818-5495 (Print)
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
Copyright © 2012 Barkat Ali Bhayo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Published: December, 2012.
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.