On some inequalities for convex functions ofhigher order
نویسندگان
چکیده
In this paper we prove some inequalities for convex function of a 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 Petrovi c's inequalities. Also, we obtain a new upper bound for the error function of the Hermite interpolating polynomial je H (x)j in terms of kf (n) k , resulting in a generalization of Mahajani inequality for diierent norm :
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