Open Access Research Article

Differences of Weighted Mixed Symmetric Means and Related Results

KhuramAli Khan1*, J Pečarić1,2 and I Perić3

Author Affiliations

1 Abdus Salam School of Mathematical Sciences, GC University, 68-B, New Muslim Town, Lahore 54600, Pakistan

2 Faculty of Textile Technology, University of Zagreb, Pierotti-jeva 6, 10000 Zagreb, Croatia

3 Faculty of Food Technology and Biotechnology, University of Zagreb, 10002 Zagreb, Croatia

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Journal of Inequalities and Applications 2010, 2010:289730 doi:10.1155/2010/289730

Published: 18 October 2010

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.