Szasz-Durrmeyer算子的逼近

对于Szasz-Durrmeyer算子，周定轩曾用光滑模ωφ^2(f,t）和ω^1(f,t)讨论了λ=1的情况，Ditzian用光滑模ω^2(f,t）和ω^1(f,t)解决了λ＝0的情况，然而对于原算子，Ditzian曾用统一光滑模ωφ^2λ（f,t)给出了一个有趣的点态逼近等价定理，统一了有关古典连续模及Ditzian-Totik模的逼近结果。对于Durrmeyer型的算子，由于一阶矩不为零，要想得到类似的结果，需要克服许多困难。本文中引入一个新算子，利用光滑模ωφ^2λ(f,t）和ω^1(f,t）之间的关系，得到了一个完美的等价定理，推广了以前的结果。

The pointwise estimate for Szasz-Durrmeyer operators

For Szasz-Durrmeyer operators, Zhou discussed the case of λ=1 byω2φ(f,t) and ω1(f,t). Ditzian solved the case of λ=0 by ω2(f,t) and ω1(f,t). However for Bernstein polynomials.Ditzian studied the pointwise approximation theorem by the opintwise modulus of smoothness ω2φ(f,t), He expanded the approximation results in classic modulus and Ditzian-Totik modulus. For Durrmeyer type, their first moment is not equal to 0. It is very difficult to obtain result similar to Bernstein polynomials. In this paper, by introducing a new operator, using the relation between ω2φ(f,t) and ω1(f,t), the obtain a pointwise equivalent theorem, which contains some previous results.