Hermite–Hadamard inequality

: dablink|Another inequality is called Hadamard's inequality.

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 : ["a", "b"] → R is convex, then

: $fleft(\; frac\{a+b\}\{2\}\; ight)\; le\; frac\{1\}\{b\; -\; a\}int\_a^b\; f(x),dx\; le\; frac\{f(a)\; +\; f(b)\}\{2\}.$

References

* Mihály Bessenyei, "The Hermite–Hadamard Inequality on Simplices", "American Mathematical Monthly", volume 115, April 2008, pages 339–345.
* Jacques Hadamard, "Étude sur les propriétés des fonctions entières et en particulier d'une fonction considérée par Riemann", "Journal de Mathématiques Pures et Appliquées", volume 58, 1893, pages 171–215.