International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 591382, 12 pages
Research Article

Some Monotonicity Results for the Ratio of Two-Parameter Symmetric Homogeneous Functions

Electric Grid Planning and Research Center, Zhejiang Province Electric Power Test and Research Institute, Hangzhou, Zhejiang 310014, China

Received 31 August 2009; Accepted 27 November 2009

Academic Editor: Feng Qi

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.


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.