Copyright © 2009 Zhen-Hang Yang. 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.

Abstract

Applying well properties of homogeneous functions, some monotonicity results for the ratio of two-parameter symmetric homogeneous functions are presented, which give an easier access to find two-parameter symmetric homogeneous means having ratio simple monotonicity properties proposed by L. Losonczi. As an application, a chain of inequalities of ratio of bivariate means is established.