Open Access

On Logarithmic Convexity for Differences of Power Means

Journal of Inequalities and Applications20082007:037359

DOI: 10.1155/2007/37359

Received: 20 July 2007

Accepted: 17 October 2007

Published: 9 January 2008

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.

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Authors’ Affiliations

(1)
Mathematical Institute, Serbian Academy of Sciences and Arts (SANU)

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Copyright

© Slavko Simic 2007

This article is published under license to BioMed Central Ltd. 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.