Baskakov型算子在H?lder空间的逼近性质

THE APPROXIMATION PROPERTIES BY BASKAKOV-TYPE OPERATORS IN H?LDER SPACE

关于H?lder(Lipschitz)范数下,不同逼近过程的收敛速度,已有许多有趣的结果.近年来,有关一些著名算子在H?lder空间的逼近定理的研究,引起人们的关注·本文主要研究Baskakov型算子在H?lder空间的应用,利用连续模与K-泛函的等价性,得到了Baskakov型算子在H?lder空间的逼近正定理.

In the case of the Holder(Lipschitz)norm,there are many interesting results on the convergence rate of different approximation processes.In recent years,the study of the approximation theorems of some well-known operators in the H¨older spaces has attracted people’s attention.In this paper,the application of Baskakov-type operators in the Holder space was discussed.Using the equivalent relation between the modulus of continuity and K-functional,the direct approximation of continuous functions in the Holder norms by Baskakov-type operators was obtained.