Hermite–Hadamard inequality

In mathematics, the Hermite–Hadamard inequality, named after Charles Hermite and Jacques Hadamard and sometimes also called Hadamard's inequality, states that if a function f : [a, b] → R is convex, then the following chain of inequalities hold: The inequality has been generalized to higher dimensions: if

⊂

is a bounded, convex domain and

is a positive convex function, then where

is a constant depending only on the dimension.