Abstract and Applied Analysis
Volume 2011 (2011), Article ID 924319, 13 pages
http://dx.doi.org/10.1155/2011/924319
Research Article

Refinements of the Lower Bounds of the Jensen Functional

Iva Franjić,1 Sadia Khalid,2 and Josip Pečarić2,3

1Faculty of Food Technology and Biotechnology, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia
2Abdus Salam School of Mathematical Sciences, GC University, 68-B, New Muslim Town, Lahore 54600, Pakistan
3Faculty of Textile Technology, University of Zagreb, Prilaz Baruna Filipovića 28A, 10000 Zagreb, Croatia

Received 1 July 2011; Accepted 4 August 2011

Academic Editor: Wing-Sum Cheung

Copyright © 2011 Iva Franjić 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 lower bounds of the functional defined as the difference of the right-hand and the left-hand side of the Jensen inequality are studied. Refinements of some previously known results are given by applying results from the theory of majorization. Furthermore, some interesting special cases are considered.