Journal of Applied Mathematics
Volume 2012 (2012), Article ID 615737, 10 pages
http://dx.doi.org/10.1155/2012/615737
Research Article
Refinements of Hermite-Hadamard Inequalities for Functions When a Power of the Absolute Value of the Second Derivative Is P-Convex
1Department of Mathematics, Lorestan University, P.O. Box 465, Khoramabad, Iran
2Department of Civil Engineering, Shahid Chamran University, P.O. Box 135, Ahvaz, Iran
3School of Engineering and Science, Victoria University, P.O. Box 14428, Melbourne, MC 8001, Australia
4School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa
Received 10 March 2012; Accepted 10 May 2012
Academic Editor: Renat Zhdanov
Copyright © 2012 A. Barani et al. 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
We extend some estimates of the right-hand side of Hermite-Hadamard-type inequalities for functions whose second derivatives absolute values are -convex. Applications to some special means are considered.