Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 037359, 8 pages
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

Academic Editor: László Losonczi

Copyright © 2007 Slavko Simic. 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.


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.