Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 037359, 8 pages
On Logarithmic Convexity for Differences of Power Means
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.