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 ƒ : [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.
Flavia-Corina Mitroi, Eleutherius Symeonidis, "The converse of the Hermite-Hadamard inequality on simplices", Expo. Math. 30 (2012), pp. 389–396. doi:10.1016/j.exmath.2012.08.011; ISSN0723-0869
Stefan Steinerberger, The Hermite-Hadamard Inequality in Higher Dimensions, The Journal of Geometric Analysis, 2019.