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Generalizations and improvements of converse Jensen's inequality for convex hulls in R^k

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

Jessen’s inequality; Lah-Ribarič inequality; convex functions; convex hull; k - simplex; barycentric coordinates; Hermite-Hadamard inequality

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