Sz（a）sz-Durrmeyer算子的点态逆结果

用一个单调函数ω(t) 为中介,利用Szasz-Durrmeyer算子导数的性质以及该算子的可换性和光滑模ωφλ(f,t)为特点,得到以下点态逼近逆定理对于f∈C0,+∞),0≤λ≤1,φ(x)=x,δn(x)=φ(x)+1/n, 若|f(x)-Sn(f,x)|≤Mω(n-1/2δ1-λn(x)),其中ω(t)≥0, ω(ut)≤C(u2+1)ω(t),则对任意t>0,有ω2φλ(f,t)≤Ct2∑0＜n≤t-1(n+1)ω(n-1)+Ct2‖f‖,ω1(f,t)≤Ct∑0＜n≤t-1ω(n-(2-λ)/(2))+Ct‖f‖.此结果推广了有关ωφ(f,t)和ω(f,t)的结果.

The pointwise converse results for Sz（a）sz-Durrmeyer operators

With an increasing function ω(t) and the properties of modulus of smoothness ωφλ(f,t),the following pointwise converse results for Szasz-Durrmeyer operators are given by using the communication and the properties of derivative about Szasz-Durrmeyer.For f∈C0,+∞),0≤λ≤1,φ(x)=x,δn(x)=φ(x)+1/n, if |f(x)-Sn(f,x)|≤Mω(n-1/2δ1-λn(x)),where ω(t)≥0, ω(ut)≤C(u2+1)ω(t),for any u>0,t>0. Then for any t>0ω2φλ(f,t)≤Ct2∑0＜n≤t-1(n+1)ω(n-1)+Ct2‖f‖,ω1(f,t)≤Ct∑0＜n≤t-1ω(n-(2-λ)/(2))+Ct‖f‖,where ω1(f,t)=sup0＜h≤t‖△hf‖C0,∞),ω2φλ(f,t)=sup|h|≤t‖△2hφλf‖C0,∞].It includes the converse results of ωφ(f,t) and ω(f,t).