【摘要】 <正> 设表示n阶Jacobi多项式;即第一类多项式,即第二类多项式;表示n阶超球面多项式。又设ω(t)是连续模函数。记 本文中c表示正的常数,但每次未必表示同一值。更多还原

【Abstract】 Let =cos (n arccos x),Pn(x) be the Legendre polynomials of degree n. And let ω(t ) be a given modulus of continuity, Hω={f|ω(f,t)≤ω(t)}.A. K. Sharma and J. Tzimbalario(J. Appro. Th., 13(1975), 431-442) considered the operators Ln,p (f, x) (p= 0, 1, 2,3) and obtained some theorems.In this paper, we prove the following theorems:Theorem 1. Let Hn(f,x) be the Hermite-Fejer operators based on thezeros of Tn(x) and x=conθ, xk=cosθk, thenTheorem 2. For all x∈[- 1, 1] and p= 1,2,3,where c is a positive constant independendent of f(x).Theorems. There exist constants N>0 and cl ,c2, (0<c1 <c2<∞) such thatfor n>N,p=1,2,3.更多还原