Journal of Inequalities and Applications 
Volume 2008 (2008), Article ID 149286, 12 pages
doi:10.1155/2008/149286
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

Recommended by Sever Dragomir

Abstract

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.