关于一个S.Bernstein过程的收敛阶

On the Convergence Order of S.Bernstein Process

1982年,Chauhan~[1]构造一个基于 x_k=cs(kπ)/(n+1),k=/(0,n+1)的插值算子 V_n(f,x)和研究了 V_n(f;x)的收敛阶.本文使用 V_n(f;x)重新证明了 Telyakovski-Gopengauz's 定理,并研究了 V_n(f;x)及其导数对 C^1函数类逼近时的收敛阶.

In 1982,Chauhan~[1] constructed an interpolation operator V.(f;x)based on the notes x_k=cos(kπ/(n+1)),k=0, n+1,and discussed the convergence order of V. (f;x).In this paper,a new proof of Te[yakovski-Gopengauz's theorem through V_n(f; x)is given,and the convergence order of V.(f;x)when using V_n^(i)(f;x)(i=0,1)to approximate f^(i)(x)C[—1,1]on[—1,1]considered.