GENERALIZATIONS AND IMPROVEMENTS OF CONVERSE JENSEN'S INEQUALITY FOR CONVEX HULLS IN ?~k

摘要

In this paper we prove generalizations and improvements of Lah-Ribari? and related inequalities for convex functions on convex hulls in ?~k and, analogously, for convex functions on k-simplices in ?~k. We also verify that one of them is a generalization and an improvement of the Hermite-Hadamard inequality for simplices.