Some inequalities of Hermite-Hadamard type for h-convex functions de…ned on convex subsets in real or complex linear spaces are given. Applications for norm inequalities are provided as well. 1. Introduction The following inequality holds for any convex function f de…ned on R (1.1) (b a)f a+ b 2 < Z b a f(x)dx < (b a) + f(b) 2 ; a; b 2 R: It was …rstly discovered by Ch. Hermite in 1881 in the j...

The superadditivity and monotonicity properties of some functionals associated with convex functions and the Hermite-Hadamard inequality in the general setting of linear spaces are investigated. Applications for norms and convex functions of a real variable are given. Some inequalities for arithmetic, geometric, harmonic, logarithmic and identric means are improved. 1. Introduction For any conv...

In this paper, we give converses of the Jensen and Edmundson– Lah–Ribarič inequalities which are more accurate than the existing ones. These converses are given in a difference form and they rely on the recent refinement of the Jensen inequality obtained via linear interpolation of a convex function. As an application, we also derive improved converse relations for generalized means, for the Hö...

Copyright q 2010 Erhan Set 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 establish some new Hermite-Hadamard-type inequalities involving product of two functions. Other integral inequalities for two functions are obtai...

In this article, a general integral identity for twice differentiable mapping involving fractional integral operators is derived. As a second, by using this identity we obtained some new generalized Hermite-Hadamards type inequalities for functions whose absolute values of second derivatives are s-convex and concave. The main results generalize the existing Hermite-Hadamard type inequalities in...