Variants of Čebyšev's inequality with applications
© M. Klariˇci´c Bakula et al. 2006
Received: 19 December 2005
Accepted: 2 April 2006
Published: 11 June 2006
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.
- Abramovich S, Klaričić Bakula M, Matić M, Pečarić J: A variant of Jensen-Steffensen's inequality and quasi-arithmetic means. Journal of Mathematical Analysis and Applications 2005,307(1):370–386. 10.1016/j.jmaa.2004.10.027MATHMathSciNetView ArticleGoogle Scholar
- Alzer H, Kovačec A: The inequality of Milne and its converse. Journal of Inequalities and Applications 2002,7(4):603–611. 10.1155/S1025583402000292MATHMathSciNetGoogle Scholar
- Lupaş A: On an inequality. Publikacije Elektrotehnickog Fakulteta Univerziteta U Beogradu. Serija Matematika i Fizika 1981, (716–734):32–34.Google Scholar
- Milne EA: Note on Rosseland's integral for the stellar absorption coefficient. Monthly Notices of the Royal Astronomical Society 1925, 85: 979–984.MATHView ArticleGoogle Scholar
- Mercer AMcD: A variant of Jensen's inequality. Journal of Inequalities in Pure and Applied Mathematics 2003,4(4):1–2. article 73 article 73MathSciNetGoogle Scholar
- Pečarić J: On the Ostrowski generalization of Čebyšev's inequality. Journal of Mathematical Analysis and Applications 1984,102(2):479–487. 10.1016/0022-247X(84)90187-2MATHMathSciNetView ArticleGoogle Scholar
- Pečarić J: On the Čebyšev inequality. Buletinul Ştiinţific şi Tehnic Institutului Politehnic "Traian Vuia" Timişoara 1980,25(39)(1):5–9 (1981).Google Scholar
- Pečarić J, Proschan F, Tong YL: Convex Functions, Partial Orderings, and Statistical Applications, Mathematics in Science and Engineering. Volume 187. Academic Press, Massachusetts; 1992:xiv+467.Google Scholar
- Rao CR: Statistical proofs of some matrix inequalities. Linear Algebra and Its Applications 2000,321(1–3):307–320.MATHMathSciNetGoogle Scholar
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.