单纯形上的q-Stancu多项式的最优逼近阶

Optimal Approximation Order for q-Stancu Operators Defined on a Simplex

构造了单纯形上的多元q-Stancu多项式,它是著名的Bernstein多项式和Stancu多项式的推广.建立该类多项式逼近连续函数的上、下界估计,进而给出其对连续函数的最优逼近阶(饱和阶)及其特征刻画.此外,还研究了该类多项式逼近连续函数的饱和类.

In this paper, a kind of multivariate linear operators, q-Stancu operators, are defined on a simplex, which generalize the famous Bernstein operators and Stancu operators. By establishing the upper and lower bound estimations of approximation order, the optimal approximation order （saturation order） and the characteristics of these operators approximating the continuous functions are characterized. Moreover, the saturation class of approximation is confirmed.