Journal of Inequalities and Applications 
Volume 2006 (2006), Article ID 39692, 13 pages
doi:10.1155/JIA/2006/39692

Variants of Čebyšev's inequality with applications

M. Klaričić Bakula,1 A. Matković,1 and J. Pečarić2

 1Department of Mathematics, Faculty of Natural Sciences, Mathematics, and Education, University of Split, Teslina 12, Split 21000, Croatia
2Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, Zagreb 10000, Croatia
Received 19 December 2005; Accepted 2 April 2006

Abstract

Several variants of Čebyšev's inequality for two monotonic n-tuples and also k≥3 nonnegative n-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.