International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 540710, 13 pages
Research Article

The Monotonicity Results for the Ratio of Certain Mixed Means and Their Applications

Power Supply Service Center, Zhejiang Electric Power Company, Electric Power Research Institute, Hangzhou 310014, China

Received 22 July 2012; Accepted 26 September 2012

Academic Editor: Edward Neuman

Copyright © 2012 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.


We continue to adopt notations and methods used in the papers illustrated by Yang (2009, 2010) to investigate the monotonicity properties of the ratio of mixed two-parameter homogeneous means. As consequences of our results, the monotonicity properties of four ratios of mixed Stolarsky means are presented, which generalize certain known results, and some known and new inequalities of ratios of means are established.