Table of Contents
Journal of Operators
Volume 2014 (2014), Article ID 382364, 5 pages
http://dx.doi.org/10.1155/2014/382364
Research Article

Inequalities of Convex Functions and Self-Adjoint Operators

Mechanical Engineering Faculty in Slavonski Brod, University of Osijek, Trg Ivane Brlić Mažuranić 2, 35000 Slavonski Brod, Croatia

Received 28 November 2013; Accepted 4 January 2014; Published 9 February 2014

Academic Editor: Palle E. Jorgensen

Copyright © 2014 Zlatko Pavić. 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 paper offers generalizations of the Jensen-Mercer inequality for self-adjoint operators and generally convex functions. The obtained results are applied to define the quasi-arithmetic operator means without using operator convexity. The version of the harmonic-geometric-arithmetic operator mean inequality is derived as an example.