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 ƒ :  → R is convex, then the following chain of inequalities hold: 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 :  → R is convex, then the following chain of inequalities hold: Suppose that −∞ < a < b < ∞, and choose n distinct values {xj}nj=1 from (a, b). Let f: → ℝ be convex, and let I denote the 'integral starting at a' operator; that is,