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Abstract and Applied Analysis
Volume 2012, Article ID 203145, 25 pages
http://dx.doi.org/10.1155/2012/203145
Research Article

The Inequalities for Quasiarithmetic Means

1Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lučića 5, 10000 Zagreb, Croatia
2Mechanical Engineering Faculty, University of Osijek, Trg Ivane Brlić Mažuranić 2, 35000 Slavonski Brod, Croatia
3Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovića 30, 10000 Zagreb, Croatia

Received 15 March 2012; Accepted 9 June 2012

Academic Editor: Sergey V. Zelik

Copyright © 2012 Jadranka Mićić et al. 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.

Abstract

Overview and refinements of the results are given for discrete, integral, functional and operator variants of inequalities for quasiarithmetic means. The general results are applied to further refinements of the power means. Jensen's inequalities have been systematically presented, from the older variants, to the most recent ones for the operators without operator convexity.