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.
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.