## A best possible Hadamard inequality.(English)Zbl 0907.26009

The classical Hadamard-Hermite inequality (for functions $$f$$ with $$f''\geq 0$$) requires that the measure be symmetric and positive. The author proves versions which require neither of these conditions; moreover, these versions are best possible, i.e., no such theorems exist with less restrictions. Inequalities with $$f''\geq 0$$ replaced by $$f^{(n)}\geq 0$$ are also investigated.

### MSC:

 26D15 Inequalities for sums, series and integrals 26D20 Other analytical inequalities