关于一类组合型三角求和算子的最佳一致逼近

On the Best Uniform Approximation of a Class of Triangle Summation Operators of Combination Type

对两类Bernstein型三角求和算子进行线性组合,构造了一个新的算子．证明了该算子在全实轴上一致收敛于任意以2π为周期的连续函数,并且得到了算子的最佳收敛阶,最后给出了算子的最高收敛阶．在收敛性方面,本文构造的新算子明显优于其他算子．

A new triangle summation operator is constructed through combining two classes of operators of Bemstein type linearly. It is proved that this operator converges to arbitrary continuous function with period on the whole axis. The best convergence order of the operator is obtained. Finally, the highest convergence order of the operator is carried out. On the aspect of convergence, the new operator constructed in this paper is superior to other operators.