关于Hermite插值算子导函数的平均收敛性

On Mean Convergence of the Derivatives of Hermite Interpolation Operator

关于算子(1.2)在最大范数意义下的收敛性已有较多研究(见[1,2)。最近,A.K.Varma,J.Prasad考虑了算子H_n(f,x)的平均收敛性,主要得到 定理A 若f∈C^I[-1,1]。

In this paper, the mean convergence of the derivatives of Hermite interpolation operator Hn(f,x) based on the zeros of Tchebycheff polynomial of the first kind is considered. It is mainly shown that