The Simultaneous Approximation And Average Errors Of Hermite Type Interpolation

In this paper, we mainly studied the mean convergence rate of simultaneous approximation by the third order Hermite interpolation based on the zeros of Chebyshev polynomials of the first kind in the weighted Lp-norm. We obtain the sharp estimation. At the same time, for the weighted Lp-norm approximation, we determine the weakly asymptotically order for the p-average errors of the Hermite-Fejer interpolation sequence based on the Chebyshev nodes on the Wiener space.