Journal of Inequalities and Applications 
Volume 2007 (2007), Article ID 37359, 8 pages
doi:10.1155/2007/37359
Research Article

On Logarithmic Convexity for Differences of Power Means

Slavko Simic

 Mathematical Institute, Serbian Academy of Sciences and Arts (SANU), Kneza Mihaila 35, Belgrade 11000, Serbia
Received 20 July 2007; Accepted 17 October 2007

Recommended by László Losonczi

Abstract

We proved a new and precise inequality between the differences of power means. As a consequence, an improvement of Jensen's inequality and a converse of Holder's inequality are obtained. Some applications in probability and information theory are also given.