运用有限振荡核方法提高正线性算子的逼近阶

An Improvement of Approximation Orders of Positive Linear Operators by Using the Method of Finite Oscillatory Kernel

为改造正线性算子以提高其逼近阶,本文利用有限振荡核方法,从常见的Fejer算子出发,构造出一种新型线性多项式算子L_n((m))(f;x),称 F-B算子,它的表达式具有良好的递推性能;通过对其收敛性和饱和性的讨论,证得F-B算子对充分光滑函数的逼近阶可达O(1/n^(2m+1)),优于Butzer与Stark的结果(O(1/n^4)),并包含Baskakov的结果(O(1/n^3)与O(1/N^5))为其特例。

We have to reform the positive linear operators in order to improve their approximation orders. In this paper, a new type of linear polynomial operators Ln(m)(f;x), called F-B operators, is constructed by using the method of finite oscillatory kernel from Fejer operator. Their representation formula has fine recurring properties. Through discussion of their convergence and saturation for sufficiently smooth fnnctions we show that the approximation orders of the F-B operators canreach which includes Baskakov's result as special case and gives better one than Butzer and Stark's when m≥2.