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Approximation by Complex Perturbed Bernstein-Type Operators
Results in Mathematics ( IF 2.2 ) Pub Date : 2020-07-10 , DOI: 10.1007/s00025-020-01244-x
Ana-Maria Acu , Gülen Başcanbaz-Tunca

In this paper we consider complex form of a modified (perturbed) Bernstein operators attached to an analytic function in a disk of radius $$R>1$$ R > 1 centered at the origin. We obtain quantitative estimates of the convergence in compact disks and exact degree of simultaneous approximation with the help of upper estimates in quantitative form, and of lower estimates obtained from a qualitative Voronovskaja type result.

中文翻译:

复杂扰动 Bernstein 类型算子的近似

在本文中,我们考虑附加到以原点为中心、半径为 $$R>1$$R>1 的圆盘中的解析函数的修正(扰动)伯恩斯坦算子的复杂形式。我们借助定量形式的上估计和从定性 Voronovskaja 类型结果获得的下估计,获得了光盘收敛的定量估计和同时近似的精确程度。
更新日期:2020-07-10
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