复平面上扩充Hermite－Fejer插值多项式的收敛性

THE CONVERGENCE PROBLEM OF MODIFIED HERMITE-FEJER INTERPOLATION POLYNOMIAL IN THE COMPLEX PLANE

得到了复平面上忽略一点导数要求的扩充Ｈｅｒｍｉｔｅ－Ｆｅｊｅｒ插值多项式在｜ｚ｜≤１上不一致收敛于ｆ（ｚ）∈Ａ（｜ｚ｜≤１）的结论，并得到了其平均收敛阶和内闭一致收敛性．

In this paper, modified Hermite-Fejer interpolation polynomial in the complex plane was studied. The conclusion that the polynomial does not converge uniformly to f(z) ∈ A(|z|≤1 ) was obtained.And the order of approximation that the polynomial converges to f(z) ∈ A(|z|≤1 ) in the sense of mean was given.