单边条件下的Taylor平均逼近

Apprxoimation by Taylor Means with One-side Condition

本文中，我们对函数加适当的条件，从而改进了Ｔａｙｌｏｒ平均逼近的阶．

Let k=ndenote the taylor means of the fouries series of 2π-periodic function f(x).In this paper we improve the estimation of approximation to f(x). The following theorem is proved.Theorem 1 Let r ≥ 0, 0 ≤α < 1,ε(h) ≥0 be a given function. If f ∈C2k and the condition holds uniformly for x∈ [0,2π],then