In this paper we point out some inequalities of Hermite-Hadamard type for double integrals of functions whose partial derivatives in absolute value are preinvex on the co-ordinates on rectangle from the plane. Our established results generalize some recent results for functions whose partial derivatives in absolute value are convex on the co-ordinates on the rectangle from the plane.

In this paper, we establish some new Hermite-Hadamard type integral inequalities involving two log-preinvex functions. Note that log-preinvex functions are nonconvex functions and include the log-convex functions as special cases. As special cases, we obtain the well known results for the convex functions.

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this article, some new generalized Hermite-Hadamard type inequalities for functions whose derivatives in absolute values are convex, concave, s-convex in the second sense, and s-concave in the second sense are established.

Some new results related of the left-hand side of the Hermite-Hadamard type inequalities for the class of mappings whose second derivatives at certain powers are s convex in the second sense are established. Also, some applications to special means of real numbers are provided. 2010 Mathematics Subject Classification: 26A51; 26D07; 26D10; 26D15

We introduce the class of (k,h) -convex functions defined on k -convex domains, and we prove some new inequalities of Hermite-Hadamard and Fejér type for such mappings. This generalizes results given for h -convex functions in [1, 17], and for s -Orlicz convex mappings in [4]. Mathematics subject classification (2010): Primary: 26A51, 26D15; Secondary: 52A30.

In this paper, new Hermite-Hadamard type inequalities for coordinated convex and co-ordinated quasi convex functions are proved in a unique way. These results generalize many results proved in earlier works for these classes of functions. Finally, applications of our results are given to estimate the product of moments of two independent continuous random variables.

In this paper, we establish several weighted inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard Fejér type integral inequality. The results presented here would provide extensions of those given in earlier works. Mathematics Subject Classification (2010): 26D15.

New Hermite-Hadamard-type integral inequalities for φ-MT-preinvex functions are obtained. Our results in special cases yield some of those results proved in recent articles concerning with the differentiable MTconvex functions. Some applications to special means and the trapezoidal formula are also considered, respectively. c ©2016 All rights reserved.

In this paper, we establish some weighted fractional inequalities for differentiable mappings whose derivatives in absolute value are convex. These results are connected with the celebrated Hermite-Hadamard-Fejér type integral inequality. The results presented here would provide extensions of those given in earlier works.