Some new classes of convex functions and inequalities

In this article, we introduce some new class of convex functions involving two arbitrary auxiliary functions h 1 ; h 2 W I ! R; which are called .h 1 ; h 2 /-convex functions. We derive some new integral inequalities for these classes of convex functions. We also discuss some special cases which can be deduced from our main results. Results obtained in this paper may be viewed as a significant refinement and improvement of the previously known results. The ideas and techniques of this work may be a starting point for future research.