中文摘要：

强φh -凸函数是强凸函数、φ凸函数与h－凸函数的推广。文章主要考虑了强φh -凸函数下的Hermite-Hadamard不等式的差值估计，推广了已知的结果。

英文摘要：

Strongly φh-convex function is a promotion of the strongly-convex functions, the φ-convex functions and the h-convex functions. Some estimations of new inequalities of Hermite-Hadamard type for strongly φh-convex functions are given by using new integral identities,which extend some known results.