摘要
本文解决了修正的Durrmeyer-Bernstein算子的特征刻划问题.对f∈C[0,1],0<α,β< 2,以下二个结论等价: (1)[x(1-x)]^(-α/2)|D_n(f,x)-f(x)|≤M_fn^(-β/2), (2)[x(1-x)]^(-α/2)|f(x+t)-2f(x)+f(x-t)|≤M/[t^2/(x(1-x))]^(β/2),其中M_f和M'_f是与n无关的常数,n∈N,0<t<1/2,x∈[t,1-t]。
In this paper we consider the relation between the rate of convergence and thesmoothness of the function that modified Durrmeyer-Bernstein operators D_n(f,x) approxi-mate. The following theorem is obtained. Theorem For f∈C[0, 1], 0<α, β<2, the following statements are equivalent:(1) [x(1-x)]^(-α/2) |D_n(f,x)-f(x)|≤M_fn^(-β/2),(2) [x(1-x)]^(-α/2) |f(x+t)-2f(x)+f(x-t)|≤M_f'[t^2/(x(1-x))]^(β/2),here M_f and M_f' are constants independent of n∈N, 0<t<1/2,x∈[t, 1-t].
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
1996年第1期75-82,共8页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
关键词
K-泛函
逼近等价定理
D-B算子
伯恩斯坦算子
Modified Durrmeyer-Bernstein Operators
K-functional
Bernstein Operators
Approximation Equivalent Theorem
