We consider integral error representation related to the Hermite interpolating polynomial and derive some new estimations of the remainder in quadrature formulae of Hermite type, using Holder’s inequality and some inequalities for the Čebyšev functional. As a special case, generalizations for the zeros of orthogonal polynomials are considered.
Aras-Gazic, G., Pečaric, J., & Vukelic, A. (2016). Integral Error Representation of Hermite Interpolating Polynomial and Related Inequalities for Quadrature Formulae. Mathematical Modelling and Analysis, 21(6), 836-851. https://doi.org/10.3846/13926292.2016.1247755
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