In this paper, we investigate the simultaneous approximation of a function f(x) and its derivative f′(x) by Hermite interpolation operator H2 n + 1(f; x) 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).
- Chevyshev polynomials
- Hermite interpolation operator
- Norm estimates
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