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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 615737, 10 pages
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.


We extend some estimates of the right-hand side of Hermite-Hadamard-type inequalities for functions whose second derivatives absolute values are 𝑃-convex. Applications to some special means are considered.