Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 289730, 16 pages
doi:10.1155/2010/289730
Research Article

Differences of Weighted Mixed Symmetric Means and Related Results

Khuram Ali Khan,1 J. Pečarić,1,2 and I. Perić3

1Abdus Salam School of Mathematical Sciences, GC University, 68-B, New Muslim Town, Lahore 54600, Pakistan
2Faculty of Textile Technology, University of Zagreb, Pierotti-jeva 6, 10000 Zagreb, Croatia
3Faculty of Food Technology and Biotechnology, University of Zagreb, 10002 Zagreb, Croatia

Received 22 June 2010; Accepted 13 October 2010

Academic Editor: Marta García-Huidobro

Copyright © 2010 Khuram Ali Khan et al. 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

Some improvements of classical Jensen's inequality are used to define the weighted mixed symmetric means. Exponential convexity and mean value theorems are proved for the differences of these improved inequalities. Related Cauchy means are also defined, and their monotonicity is established as an application.