Simultaneous Approximation Of The Two Kinds 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 the Chebyshev polynomials of the first kind. Furthermore, we give a Quasi- Hermite interpolation operator which is based on the zeros of the Chebyshev polynomials of the second kind and discuss its mean convergence rate of derivative approximation. At the same time, we research the simultaneous approximation convergence rate of Lagrange interpolation operator (which is based on the zeros of the Chebyshev polynomials of the first kind) on the weighted L-p norm. All our results are sharp .