Skip to main content
Journal of Inequalities and Applications
Download PDF
  • Research Article
  • Open access
  • Published:

On Logarithmic Convexity for Differences of Power Means

Journal of Inequalities and Applications volume 2007, Article number: 037359 (2008) Cite this article

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.

[123456]

References

  1. Hardy GH, Littlewood JE, Pólya G: Inequalities. Cambridge University Press, Cambridge, UK; 1978.

    Google Scholar 

  2. Mitrinović DS: Analytic Inequalities, Die Grundlehren der mathematischen Wisenschaften, Band 1965. Springer, Berlin, Germany; 1970:xii+400.

    Google Scholar 

  3. Rossberg H-J, Jesiak B, Siegel G: Analytic Methods of Probability Theory, Mathematische Monographien. Volume 67. Akademie, Berlin, Germany; 1985:311.

    Google Scholar 

  4. Kullback S, Leibler RA: On information and sufficiency. Annals of Mathematical Statistics 1951,22(1):79–86. 10.1214/aoms/1177729694

    Article  MathSciNet  MATH  Google Scholar 

  5. MacMahon PA: Combinatory Analysis. Chelsea, New York, NY, USA; 1960:xix+302+xix+340.

    MATH  Google Scholar 

  6. Pečarić JE, Proschan F, Tong YL: Convex Functions, Partial Orderings, and Statistical Applications, Mathematics in Science and Engineering. Volume 187. Academic Press, Boston, Mass, USA; 1992:xiv+467.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematical Institute, Serbian Academy of Sciences and Arts (SANU), Kneza Mihaila 35, Belgrade, 11000, Serbia

    Slavko Simic

Authors
  1. Slavko Simic
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Slavko Simic.

Rights and permissions

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.

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/2007/37359

Keywords