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Hermite–Hadamard inequality - Wikipedia, the free encyclopedia

Hermite–Hadamard inequality

From Wikipedia, the free encyclopedia

In mathematics, the Hermite–Hadarmard inequality, named after Charles Hermite and Jacques Hadamard and sometimes also called Hadamard's inequality, states that if a function ƒ : [ab] → R is convex, then

 f\left( \frac{a+b}{2}\right) \le \frac{1}{b - a}\int_a^b f(x)\,dx \le \frac{f(a) + f(b)}{2}.

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