论文标题
单元磁盘上的一类Bernstein型操作员
A class of Bernstein-type operators on the unit disk
论文作者
论文摘要
我们构建和研究作用于单位磁盘上定义的双变量功能的伯恩斯坦型线性算子的序列。为此，我们在域转换下研究了伯恩斯坦型操作员，我们分析了双变量的伯恩斯坦 - 斯坦科运营商，并通过磁盘象限上介绍了伯恩斯坦型操作员，该函数的不断变化。我们陈述了连续功能的收敛结果，并估计收敛速度。最后，给出了一些有趣的数值示例，并使用移动的伯恩斯坦 - 斯坦图（Bernstein-Stancu）和伯恩斯坦型操作员在磁盘象限上进行比较。
We construct and study sequences of linear operators of Bernstein-type acting on bivariate functions defined on the unit disk. To this end, we study Bernstein-type operators under a domain transformation, we analyse the bivariate Bernstein-Stancu operators, and we introduce Bernstein-type operators on disk quadrants by means of continuously differentiable transformations of the function. We state convergence results for continuous functions and we estimate the rate of convergence. Finally some interesting numerical examples are given, comparing approximations using the shifted Bernstein-Stancu and the Bernstein-type operator on disk quadrants.
