A best possible Hadamard inequality. (English) Zbl 0907.26009

Fink, A. M.

Math. Inequal. Appl. 1, No. 2, 223-230 (1998).

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.

Reviewer: I.Raşa (Cluj-Napoca)

MSC:

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

Keywords:

Hadamard-Hermite inequality