Abstract and Applied Analysis
Volume 2010 (2010), Article ID 830163, 16 pages
Research Article

Necessary and Sufficient Conditions for Schur Geometrical Convexity of the Four-Parameter Homogeneous Means

System Division, Zhejiang Province Electric Power Test and Research Institute, Hangzhou, Zhejiang 310014, China

Received 20 February 2010; Revised 17 March 2010; Accepted 23 March 2010

Academic Editor: Roman Šimon Hilscher

Copyright © 2010 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.


The necessary and sufficient conditions for Schur geometrical convexity of the four-parameter means are given. This gives a unified treatment for Schur geometrical convexity of Stolarsky and Gini means.