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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
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