The Derivative Approximation Of Interpolation Operators

In this paper, we mainly consider the derivative approximation of continuous differentiable functions by the Hermite interpolation which is based on the zeros of Chebyshev polynomials of the second kinds. We obtain the sharp estimate which is in term of the best approximation. At the same time,we discuss the average errors of Hermite-Fejer interpolation operator and the Grunwald interpolation operator which are based on the zeros of the Chebyshev polynomials of the second kinds on the Wiener space. We obtained the strongly asymptotic order.