title: Convergence and norm estimates of Hermite interpolation at zeros of Chevyshev polynomials.
abstract: In this paper, we investigate the simultaneous approximation of a functionf(x) and its derivative [Formula: see text] by Hermite interpolation operator [Formula: see text] based on Chevyshev polynomials. We also establish general theorem on extreme points for Hermite interpolation operator. Some results are considered to be an improvement over those obtained in Al-Khaled and Khalil (Numer Funct Anal Optim 21(5-6): 579-588, 2000), while others agrees with Pottinger's results (Pottinger in Z Agnew Math Mech 56: T310-T311, 1976).
authors.affiliation: Mathematics and Statistics, Jordan University of Science and Technology, P.O. Box 3030, Irbid, 22110 Jordan.
authors.forename: Kamel
authors.initials: K
authors.lastname: Al-Khaled
authors.affiliation: Mathematics and Statistics, Jordan University of Science and Technology, P.O. Box 3030, Irbid, 22110 Jordan.
authors.forename: Marwan
authors.initials: M
authors.lastname: Alquran
keywords: Chevyshev polynomials; Hermite interpolation operator; Norm estimates