Several integral inequalities for strongly $(\alpha, m)$-convex functions with modulus

In the paper, the authors introduce the concept of strongly $(\alpha, m)$-convex function with modulus, establish several new integral identities, and, by virtue of these newly-identities and H\"older's inequality, present some new integral inequalities of the Hermite--Hadamard type for strongly $(\alpha, m)$-convex functions with modulus.