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On Logarithmic Convexity for Differences of Power Means

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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Correspondence to Slavko Simic.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Simic, S. On Logarithmic Convexity for Differences of Power Means. J Inequal Appl 2007, 037359 (2008). https://doi.org/10.1155/2007/37359

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Keywords

  • Information Theory
  • Precise Inequality
  • Logarithmic Convexity
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