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Improvements and Generalizations of Converse Jensens Inequality and Related Results

In this talk we prove generalizations and improvements of Converse Jensens inequality for convex functions de ned on convex hulls. As consequences we get generalizations and improvements of the Hermite-Hadamard inequality for convex functions de ned on k-simplices in Rk. We also present some related results which generalize and improve results from A. Matkovic, J. Pecaric , A variant of Jensens inequality for convex functions of several variables, J. Math. Ineq., 1, 1 (2007), 4551.

Jensens inequality; Converse Jensens inequality; convex hull; convex functions; Hermite-Hadamard inequality; k-simplex; barycentric coordinates

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