We derive some new integral identities for differentiable functions. Then using these auxiliary results, we obtain new Hermite-Hadamard type inequalities for differentiable p-convex functions. Some special cases are also discussed.

We first introduce the notion of operator (h 1 , h 2)-preinvex on the coordinates. After this some new two dimensional version of integral inequalities of Hermite-Hadamard type associated with this new class of operator (h 1 , h 2)-preinvex are obtained. Some new and novel particular cases are also discussed.

A new class of harmonic convex function depending on given functions which is called as "approximately harmonic h-convex functions" is introduced. With the discussion of special cases it is shown that this class unifies other classes of approximately harmonic h-convex function. Some associated integral inequalities with these new classes of harmonic convexity are also obtained. Several special cases of the main results are also discussed.