On some inequality of Hermite-Hadamard type
Abstract. It is well-known that the left term of the classical Hermite-Hadamard inequality is closer to the integral mean value than the right one. We show that in the multivariate case it is not true. Moreover, we introduce some related inequality comparing the methods of the approximate integration, which is optimal. We also present its counterpart of Fejér type.
Keywords: convex function, Hermite-Hadamard inequality, Fejér inequality, simplex, approximate integration.
Mathematics Subject Classification: 26D15, 26A51, 26B25, 65D30, 65D32.