  In a recent paper [9], Ozdemir, Tunc and Akdemir defined two new classes of
convex functions with which they proved some Hermite-Hadamard type
inequalities. As an Open problem, they asked for conditions under which the
composition of two functions belong to their newly defined class of convex
functions and if Hermite-Hadamard type inequalities can be obtained. In this
paper, we respond to the Open problems and prove some new Hermite-Hadamard
inequalities for twice differentiable composition whose second derivative is
$((h-s)_{2}, I)$-convex. Our results are applied to some special means of real
numbers.
