Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 107950, 13 pages
doi:10.1155/2010/107950
Research Article
Iterative Refinements of the Hermite-Hadamard Inequality, Applications to the Standard Means
1Research Group in Mathematical Inequalities and Applications, School of Engineering and Science, Victoria University, P.O. Box 14428, Melbourne City, MC 8001, Australia
2School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg 2000, South Africa
3Applied Functional Analysis Team, AFACSI Laboratory, Faculty of Science, Moulay Ismaïl University, P.O. Box 11201, Meknès, Morocco
Received 29 July 2010; Accepted 19 October 2010
Academic Editor: László A. Losonczi
Copyright © 2010 Sever S. Dragomir and Mustapha Raïssouli. 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
Two adjacent recursive processes converging to the mean value of a real-valued convex function are given. Refinements of the Hermite-Hadamard inequality are obtained. Some applications to the special means are discussed. A brief extension for convex mappings with variables in a linear space is also provided.