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

Abstract

Abstract. 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 HermiteHadamard inequalities are presented. As a special case, generalizations for the zeros of orthogonal polynomials are considered.Mathematics subject classification (2010): Primary 26D15; Secondary 26D07, 26A51.

Integral Error Representation of Hermite Interpolating Polynomial and Related Inequalities for Quadrature Formulae

“…In [4] M. Bessenyei and Zs. Páles considered the following Gauss type quadrature formulae where the coefficients and the base points are to be determined so that be exact when f is a polynomial of degree at most 2n − 1, 2n, 2n and 2n + 1, respectively (see also [3]…”