As an important type of polynomial approximation, approximation of functions by Bernstein operators is an important topic in approximation theory and computational theory. This paper gives global and pointwise estimat...As an important type of polynomial approximation, approximation of functions by Bernstein operators is an important topic in approximation theory and computational theory. This paper gives global and pointwise estimates for weighted approxi-mation of functions with singularities by Bernstein operators. The main results are the Jackson's estimates of functions f∈(Ww,λ)2 and f∈Cw, which extends the result of (Della Vecchia et al., 2004).展开更多
设f(x)在[0,∞)的每一有限子区间上为有界变差函数,作用在f(x)上的Szasz—Mirakyan算子和Baskakov算子分别为:S,(f,x)=sum from k=0 to ∞ (f(k/n)e^(nx)((nx)~k)/kl),V_n(f,x)=sum from k=0 to ∞ (f(k/n)((n+k-1)/k))x^k/(1+x)^(n+k))...设f(x)在[0,∞)的每一有限子区间上为有界变差函数,作用在f(x)上的Szasz—Mirakyan算子和Baskakov算子分别为:S,(f,x)=sum from k=0 to ∞ (f(k/n)e^(nx)((nx)~k)/kl),V_n(f,x)=sum from k=0 to ∞ (f(k/n)((n+k-1)/k))x^k/(1+x)^(n+k)) Fuhua Cheng借助Bojanic的方法得出了S_n(f,x)对f(x)的点态逼近度。本文在学习与参考[2]的基础上,更多地应用概率方法,来研究V_n(f,x)对f(x)的点态逼近度。在处理尾部时,我们得到了一个一般性的结果(文中的引理5),它不仅可以用来证明本文的定理1,而且也适用于其他算子,从而简化了[2]中的计算。展开更多
文摘As an important type of polynomial approximation, approximation of functions by Bernstein operators is an important topic in approximation theory and computational theory. This paper gives global and pointwise estimates for weighted approxi-mation of functions with singularities by Bernstein operators. The main results are the Jackson's estimates of functions f∈(Ww,λ)2 and f∈Cw, which extends the result of (Della Vecchia et al., 2004).
文摘设f(x)在[0,∞)的每一有限子区间上为有界变差函数,作用在f(x)上的Szasz—Mirakyan算子和Baskakov算子分别为:S,(f,x)=sum from k=0 to ∞ (f(k/n)e^(nx)((nx)~k)/kl),V_n(f,x)=sum from k=0 to ∞ (f(k/n)((n+k-1)/k))x^k/(1+x)^(n+k)) Fuhua Cheng借助Bojanic的方法得出了S_n(f,x)对f(x)的点态逼近度。本文在学习与参考[2]的基础上,更多地应用概率方法,来研究V_n(f,x)对f(x)的点态逼近度。在处理尾部时,我们得到了一个一般性的结果(文中的引理5),它不仅可以用来证明本文的定理1,而且也适用于其他算子,从而简化了[2]中的计算。
