用Newman型有理算子对|x|的逼近的渐近性质(英文)

The Asymptotic Property of Approximation to |x| by Newman Type Rational Operators

设p(x)=∏k=1n=1((k/n)r+z),0<r≤1,Hn,r(x)=x(p(x)-p(-x))/(p(x)+p(-x)).本文给出max|x|≤1||x|-Hn,r(x)| 的渐近式.

Let p(x) =∏k=1n=1((k/n)r+z),0<r≤1,Hn,r(x)=x(p(x)-p(-x))/(p(x)+p(-x)).The present note gives the asymptotic formula of max ||x| - Hn,r(x)|.