The Hermite-Hadamard inequality can be easily extended to the case of twice differentiable functions with bounded second derivative. Precisely, if then
The paper under review contains extensions of the Hermite-Hadamard inequality to the context of functions with bounded derivatives of th order. For example, if is an -times differentiable function with then it is proved that
where Further extensions are obtained via the concept of harmonic sequence of polynomials.