BernStein算子和Bernstein-Kantorovic算子的∧_(ω)(A)类保持性质

On the Property of Bernstein and Bernstein-Kantorovic Operators Preserving the Class A_(ω)(A)

设ω(x)是[0,1]上的上凸连续模函数,记A_ω(A)={f∈[0,1]:ω(f,x)≤A_ω(x)},本文得到f∈A_ω(A)的充要条件是L_n(f)∈A_ω(A),其中L_n表示Bernstrein算子B_n或BernsteinKantorovi(?)算子K_n。

Let ω(x) be any convex modulus of continuity andAω(A)={f(?)c[0, 1]:ω(f ,x)≤<Aω(x)}.In this paper we obtain the following result: f(?)Aω(A)(?)L_n(f)(?)Aω(A), n=1,2,…, Where Ln is Bernstein polynomials or Bernstein-Kantorovi(?) polynomials,