Inequalities of the Hermite-Hadamard type involving numerical differentiation formulas

Andrzej Olbryś, Tomasz Szostok

We observe that the Hermite-Hadamard inequality written in the form $$f\left(\frac{x+y}{2}\right)\le \frac{F(y)-F(x)}{y-x}\le \frac{f(x)+f(y)}{2}$$ may be viewed as an inequality b…