关于K阶Bernstein—Kantorovi算子

THE Kn-ORDER BERNTEIN-KANTOROVI OPERATORS

本文给出了 km 阶 Bernstein-kantorovic 算子B_n^k_n(f.x)=(n+k_n)~k_n sum from v=0 to n integral from 0…to 1/a+k_n integral from 0…to 1/a+k_n f(v/n+k_n+S1+…+S_k_n)ds1…ds_k_npnv(x)其中正整数列 k_n 满足 n k_n/n=0,而 f(x)eL_[0,1],pnv(x)=(n/v)xv(i-x)^(n-v)。而且讨论了当n k_u/n=0时算子 B_n^(k_u) 在 Orlicz 空间中的逼近阶.

In this paper,the Kn-order Berstein-Kantorovic operators B_n^(k_n)(f,x)=(n+k_n)~k_n sum from v=0 to n integral from n=0 to (1/n+k_n) f((v/n+k_n)+s_1+…+s_k_n)ds_1…ds_k_n P_n■(x)are given,where Pn_v(x)=(n/v)x(1-x),lim(k_n/n)=0,f(x)∈L[0,1]and the degree ofapproximation by this operators in Orlicz spaces are studied.