engleski

On some inequalities for convex functions of higher order II

In this paper we prove some inequalities for convex function of higher order. The well known Hermite interpolating polynomial leads us to a converse of Jensen inequality for a regular, signed measure and, as a consequence, a generalization of Hadamard and Petrović's inequalities. Also, we obtain a new upper bound for the error function of the Hermite interpolating polynomial|eH(x)| in terms of different norm ni of ||f^(n)||ni, resulting in a generalization of Mahajani inequality for different norm ni.

Jensen inequality; Hadamard inequality; Petrović inequality; Hermite's polynomial; (n)-convex function

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