Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 167091, 18 pages
doi:10.1155/2010/167091
Research Article

On Generalizations of Grüss Inequality in Inner Product Spaces and Applications

Aristides I. Kechriniotis1 and Konstantinos K. Delibasis2

1Department of Electronics, Technological Educational Institute of Lamia, 35100 Lamia, Greece
2Department of Computer Science and Biomedical Informatics, University of Central Greece, 35100 Lamia, Greece

Received 23 December 2009; Revised 7 May 2010; Accepted 15 June 2010

Academic Editor: S. S. Dragomir

Copyright © 2010 Aristides I. Kechriniotis and Konstantinos K. Delibasis. 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

Using a Kurepa's result for Gramians, we achieve refinements of well-known generalizations of Grüss inequality in inner product spaces. These results are further applied in L2(a,b) to derive improvements of some published trapezoid-Grüss and Ostrowki-Grüss type inequalities. Refinements of the discrete version of Grüss inequality as well as a reverse of the Schwarz inequality are also given.