Iterative Refinements of the Hermite-Hadamard Inequality, Applications to the Standard Means
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
Journal of Inequalities and Applications 2010, 2010:107950 doi:10.1155/2010/107950Published: 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.