关于Szsz-Durrmeyer-Bzier算子的点态逼近

Pointwise Approximation for Szsz-Durrmeyer-Bzier Operators

Bzier型算子是一些著名算子的推广,已有研究成果主要是对有界变差函数的逼近,而对于应用光滑模研究其中心逼近定理的结果很少。本文利用一阶Ditzian-Totik模得到了Szsz-Durrmeyer-Bzier算子点态逼近的正、逆定理及等价定理这一完美的逼近结果。

The Bézier type operators are generalizations of some well-known operators. For bounded variation functions many approximation results have been obtained, but the results of central approximation theorem by using modulus of smoothness are few. We give the direct and inverse approximation theorems and equivalent theorem for Szasz-Durrmeyer-Bézier operators with the first order DitzianTotik modulus of smoothness.