复真$α-$ Bernstein-Durrmeyer算子的逼近性质
Approximation properties of complex genuine $α-$Bernstein-Durrmeyer operators
摘要：
本文提出了一个依赖于非负实参数$α.$的Bernstein-Durrmeyer型算子的复形式，给出了这类算子及其导数在紧致圆盘上对解析函数的逼近的定量上界、Voronovskaja型结果和精确阶.这些结果验证了复真$α-$ Bernstein-Durrmeyer型算子的逼近性质从实区间到复平面紧致圆盘的推广.
英文摘要：
Herein we propose a complex form of a genuine Bernstein-Durrmeyer type operators depending on a non-negative real parameter $α.$ We present the quantitative upper bound, Voronovskaja type result and exact order of approximation for these operators and for their derivatives attached to analytic functions on compact disks. These results validate the extension of approximation properties of complex genuine $α-$Bernstein-Durrmeyer type operators from real intervals to compact disks in the complex plane.
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