In the paper, the famous Hermite-Hadamard integral inequality for convex functions is generalized to and refined as inequalities for n-time differentiable functions which are (α, m)-convex. MSC: Primary 26D15; secondary 26A51; 41A55

In this paper, the authors introduce a new concept " 11 ( , ) sm -22 ( , ) sm -convex function on co-ordinates" and establish some inequalities for 11 ( , ) sm -22 ( , ) sm -convex functions of 2-variables on the co-ordinates.

In the paper, the authors define a new notion of "HT-convex function", present some Hadamard-type inequalities for the new class of HT-convex functions and for the product of any two HT-convex functions, and derive some inequalities for the arithmetic mean and the p-logarithmic mean. These results generalize corresponding ones for HA-convex functions and MT-convex functions.

In this paper, the notion of (s, m)-P -convex functions on the co-ordinates is introduced and several integral inequalities of the Hermite-Hadamard type for co-ordinated (s, m)-P -convex functions are established.

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