Differences of Weighted Mixed Symmetric Means and Related Results
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
Journal of Inequalities and Applications 2010, 2010:289730 doi:10.1155/2010/289730Published: 18 October 2010
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.