Open Access

Variants of Čebyšev's inequality with applications

Journal of Inequalities and Applications20062006:39692

DOI: 10.1155/JIA/2006/39692

Received: 19 December 2005

Accepted: 2 April 2006

Published: 11 June 2006

Abstract

Several variants of Čebyšev's inequality for two monotonic -tuples and also nonnegative -tuples monotonic in the same direction are presented. Immediately after that their refinements of Ostrowski's type are given. Obtained results are used to prove generalizations of discrete Milne's inequality and its converse in which weights satisfy conditions as in the Jensen-Steffensen inequality.

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Authors’ Affiliations

(1)
Department of Mathematics, Faculty of Natural Sciences, Mathematics, and Education, University of Split
(2)
Faculty of Textile Technology, University of Zagreb

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Copyright

© M. Klariˇci´c Bakula et al. 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.