Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 149286, 12 pages
Research Article

On the Monotonicity and Log-Convexity of a Four-Parameter Homogeneous Mean

Zhen-Hang Yang

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

Received 13 April 2008; Accepted 29 July 2008

Academic Editor: Sever Dragomir

Copyright © 2008 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.


A four-parameter homogeneous mean 𝐅(p,q;r,s;a,b) is defined by another approach. The criterion of its monotonicity and logarithmically convexity is presented, and three refined chains of inequalities for two-parameter mean values are deduced which contain many new and classical inequalities for means.