Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 496821, 15 pages
doi:10.1155/2010/496821
Research Article

Some Reverses of the Jensen Inequality for Functions of Selfadjoint Operators in Hilbert Spaces

S. S. Dragomir1,2

1Mathematics, School of Engineering & Science, Victoria University, P.O. Box 14428, Melbourne, MC 8001, Australia
2School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa

Received 22 September 2009; Accepted 23 April 2010

Academic Editor: Patricia J.Y. Wong

Copyright © 2010 S. S. Dragomir. 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

Some reverses of the Jensen inequality for functions of self-adjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given. Applications for particular cases of interest are also provided.