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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 258108, 12 pages
http://dx.doi.org/10.1155/2014/258108
Research Article

Schur -Power Convexity of a Class of Multiplicatively Convex Functions and Applications

1School of Mathematics and Statistics, Hefei Normal University, Hefei 230601, China
2Department of Mathematics and Physics, Anhui Xinhua University, Hefei 230088, China

Received 14 January 2014; Revised 2 April 2014; Accepted 23 April 2014; Published 20 May 2014

Academic Editor: Marco Sabatini

Copyright © 2014 Wen Wang and Shiguo 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.

Abstract

We investigate the conditions under which the symmetric functions are Schur -power convex for and . As a consequence, we prove that these functions are Schur geometrically convex and Schur harmonically convex, which generalizes some known results. By applying the theory of majorization, several inequalities involving the th power mean and the arithmetic, the geometric, or the harmonic means are presented.