Open Access

The inequality of Milne and its converse II

Journal of Inequalities and Applications20062006:21572

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

Received: 15 September 2004

Accepted: 19 September 2004

Published: 3 January 2006

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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Authors’ Affiliations

(1)
(2)
Departamento de Matemática, Universidade de Coimbra

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Copyright

© Alzer and Kovačec 2006

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.