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Cauchy’s error representation of Hermite interpolating polynomial and related results

In this paper we consider convex functions of higher order. Using the Cauchy’s error representation of Hermite interpolating polynomial the results concerning to the Hermite-Hadamard inequalities are presented. As a special case, generalizations for the zeros of orthogonal polynomials are considered.

n-convex function ; Hermite interpolating polynomial ; Hermite-Hadamard inequality ; orthogonal polynomials.

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