Journal of Inequalities and Applications
Volume 2011 (2011), Article ID 581918, 25 pages
doi:10.1155/2011/581918
Research Article
Schur-Convexity of Averages of Convex Functions
1Department of Mathematics, Faculty of Civil Engineering, University of Zagreb, Kačićeva 26, 10000 Zagreb, Croatia
2Faculty of Food Technology and Biotechnology, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia
3Abdus Salam School of Mathematical Sciences, 68-B, New Muslim Town, Lahore 54600, Pakistan
4Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovića 28a, 10000 Zagreb, Croatia
Received 12 November 2010; Accepted 11 January 2011
Academic Editor: Matti K. Vuorinen
Copyright © 2011 Vera Čuljak 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
The object is to give an overview of the study of Schur-convexity of various means and functions and to contribute to the subject with some new results. First, Schur-convexity of the generalized integral and weighted integral quasiarithmetic mean is studied. Relation to some already published results is established, and some applications of the extended result are given. Furthermore, Schur-convexity of functions connected to the Hermite-Hadamard inequality is investigated. Finally, some results on convexity and Schur-convexity involving divided difference are considered.