title: Improvements of the Hermite-Hadamard inequality for the simplex.
abstract: In this study, the simplex whose vertices are barycenters of the given simplex facets plays an essential role. The article provides an extension of the Hermite-Hadamard inequality from the simplex barycenter to any point of the inscribed simplex except its vertices. A two-sided refinement of the generalized inequality is obtained in completion of this work.
authors.affiliation: Department of Mathematics, Mechanical Engineering Faculty in Slavonski Brod, University of Osijek, Slavonski Brod, 35000 Croatia.
authors.forename: Zlatko
authors.initials: Z
authors.lastname: Pavić
keywords: convex combination; simplex; the Hermite-Hadamard inequality