In this paper, the concept of the $(p,h)$-convex function is introduced, which generalizes the $p$-convex function and the $h$-convex function, and Hermite-Hadamard type inequalities for $(p,h)$-convex functions on $\mathbb{R}^n$ are established. Furthermore, some mappings related to the above inequalities are studied and some known results are generalized.