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The inequality of Milne and its converse II

Journal of Inequalities and Applications volume 2006, Article number: 21572 (2006) Cite this article

Abstract

We prove the following let, and be real numbers, and let be positive real numbers with. The inequalities hold for all real numbers if and only if and. Furthermore, we provide a matrix version. The first inequality (with and) is a discrete counterpart of an integral inequality published by E. A. Milne in 1925.

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References

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Authors and Affiliations

  1. Morsbacher Street 10, Waldbröl, 51545, Germany

    Horst Alzer

  2. Departamento de Matemática, Universidade de Coimbra, Coimbra, 3001-454, Portugal

    Alexander Kovačec

Authors
  1. Horst Alzer
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  2. Alexander Kovačec
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Correspondence to Horst Alzer.

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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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Alzer, H., Kovačec, A. The inequality of Milne and its converse II. J Inequal Appl 2006, 21572 (2006). https://doi.org/10.1155/JIA/2006/21572

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  • DOI: https://doi.org/10.1155/JIA/2006/21572

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