Open Access Research

Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex

Ali Barani1*, Amir G Ghazanfari1 and Sever S Dragomir23

Author Affiliations

1 Department of Mathematics, Lorestan University, P.O. Box 465, Khoramabad, Iran

2 School of Engineering and Science, Victoria University, P.O. Box 14428, Melbourne City, VIC, 8001, Australia

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

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Journal of Inequalities and Applications 2012, 2012:247  doi:10.1186/1029-242X-2012-247

Published: 29 October 2012

Abstract

In this article, we extend some estimates of the right-hand side of a Hermite-Hadamard-type inequality for preinvex functions. Then, a generalization to functions of several variables on invex subsets of is introduced.

Keywords:
Hermite-Hadamard inequality; invex sets; preinvex functions