Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 323615, 15 pages
doi:10.1155/2009/323615
Research Article

On Some Improvements of the Jensen Inequality with Some Applications

M. Adil Khan,1 M. Anwar,1 J. Jakšetić,2 and J. Pečarić1,3

1Abdus Salam School of Mathematical Sciences, GC University, 5400 Lahore, Pakistan
2Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, 1000 Zagreb, Croatia
3Faculty of Textile Technology, University of Zagreb, 1000 Zagreb, Croatia

Received 23 April 2009; Accepted 10 August 2009

Academic Editor: Sever Silvestru Dragomir

Copyright © 2009 M. Adil Khan 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

An improvement of the Jensen inequality for convex and monotone function is given as well as various applications for mean. Similar results for related inequalities of the Jensen type are also obtained. Also some applications of the Cauchy mean and the Jensen inequality are discussed.