Abstract and Applied Analysis
Volume 2011 (2011), Article ID 358981, 14 pages
http://dx.doi.org/10.1155/2011/358981
Research Article

Extension of Jensen's Inequality for Operators without Operator Convexity

Jadranka Mićić,1 Zlatko Pavić,2 and Josip Pečarić3

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 7 March 2011; Accepted 13 April 2011

Academic Editor: Nikolaos Papageorgiou

Copyright © 2011 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

We give an extension of Jensen's inequality for 𝑛 -tuples of self-adjoint operators, unital 𝑛 -tuples of positive linear mappings, and real-valued continuous convex functions with conditions on the operators' bounds. We also study operator quasiarithmetic means under the same conditions.