Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 628051, 16 pages
doi:10.1155/2009/628051
Research Article

Cauchy Means of the Popoviciu Type

Matloob Anwar,1 Naveed Latif,1 and J. Pečarić1,2

1Abdus Salam School of Mathematical Sciences, 68-B New Muslim Town, GC University, Lahore 54000, Pakistan
2Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, Zagreb 10000, Croatia

Received 9 October 2008; Accepted 2 February 2009

Academic Editor: Wing-Sum Cheung

Copyright © 2009 Matloob Anwar 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

We discuss log-convexity for the differences of the Popoviciu inequalities and introduce some mean value theorems and related results. Also we give the Cauchy means of the Popoviciu type and we show that these means are monotonic.