In this note, we give a counterexample to show that Hadamard's inequality does not hold on a polyhedron in multi-dimensional Euclidean space. Then we give a sufficient condition on the polyhedron for Hadamard's inequality to hold. Finally, we provide an approach to create a large class of polyhedra on which Hadamard's inequality is true. © 2007 Elsevier Ltd. All rights reserved.
Yang, W. H. (2008). A generalization of Hadamard’s inequality for convex functions. Applied Mathematics Letters, 21(3), 254–257. https://doi.org/10.1016/j.aml.2007.02.024