摘要
本文利用点态光滑模ω(?)λ2r(f,t)研究了Bernstein算子的r阶线性组合的点态逼近.当1-1/r≤λ≤1时,用ω(?)λ2r(f,t)给出了—个点态逼近等价定理.且用反例说明了当0≤λ<1-1/r 时,此结论不成立.但若限制0<α<min{2(r+1)/2-λ,2r},则用ω(?)λ2r(f,t)给出了一个等价定理.所得结果统一了已有的关于古典光滑模和Ditzian-Totik模的结果.
Using the pointwise modulus ω^2r φλ（f,t）,we discuss the approximation theorem for the r order linear combinations of Bernstein-Durrmerer operators.When 1-1/r≤λ≤1, we give an equivalent theorem by ω^2r φλ（f,t）,and show that it does not hold for 0≤λ〈1-1/r by a counterexample. But if 0〈α〈min{2（r＋1）/2-λ,2r} we obtain the similar results by ω^2r φλ（f,t）,The results contain the results about the classical modulus of smoothness and the Ditzian-Totik modulus.
基金
河北省自然科学基金(A2004000137)河北省博士基金(B2001119)河北师范大学博士基金(L2000b02)
