Hermite-Fejr插值算子的平均收敛准则

MEAN CONVERGENCE CRITERIA FOR HERMITE FEJ E′ R INTERPOLATING OPERATOR

给出了一个有用的判断Ｈｅｒｍｉｔｅ－Ｆｅｊéｒ插值算子Ｈｎ（ｆ，ｘ）平均收敛准则，即Ｈｎ（ｆ，ｘ）依范数收敛于ｆ（ｘ）的充分必要条件是：Ｈｎ（ｆ，ｘ）一致有界（对一切ｎ）并且Ｈｎ（ｆ，ｘｋ）依范数收敛于ｘｋ（ｋ＝１，２）．

In this paper we give an useful mean convergence criteria for Hermite Fejér interpolating operator. It is Hermite Fejér interpolating operator mean convergence for very continous function if and only if the norms of the operator are uniformly bounded for all n and mean convergence for x and x 2 .