关于Timan定理的一点注记

A NOTE ON TIMAN THEOREM

本文研究了连续函数的最佳逼近多项式的点态逼近性质.通过一个具体函数的连续模估计,得到最佳逼近多项式的点态逼近阶估计,并且存在连续函数使得最佳逼近多项式能够满足Timan定理.

In this paper, we consider the pointwise approximation properties of continuous functions. We obtain the estimate of the approximaton order of some continuous function by using its modulus of continuity. The estimate shows that the polynomials of best uniform approxiation to continuous function can also satisfy the Timan theorem for polynomial approximation of continuous functions.