SpringerOpen Newsletter

Receive periodic news and updates relating to SpringerOpen.

Open Access Open Badges Research Article

Iterative Refinements of the Hermite-Hadamard Inequality, Applications to the Standard Means

SeverS Dragomir12 and Mustapha Raïssouli3*

Author Affiliations

1 Research Group in Mathematical Inequalities and Applications, School of Engineering and Science, Victoria University, P.O. Box 14428, Melbourne City, MC 8001, Australia

2 School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg 2000, South Africa

3 Applied Functional Analysis Team, AFACSI Laboratory, Faculty of Science, Moulay Ismaïl University, P.O. Box 11201, Meknès, Morocco

For all author emails, please log on.

Journal of Inequalities and Applications 2010, 2010:107950  doi:10.1155/2010/107950

Published: 24 October 2010


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.