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| 摘要: |
| 本文研究了复q-Bernstein-Durrmeyer型算子在紧圆盘上的相关性质,利用高阶Cauchy积分公式、泰勒展式和Bernstein不等式等方法,获得了该算子在紧圆盘上的同时逼近和在封闭单位圆盘上的Voronovskaja型定理,并给出了q-Bernstein-Durrmeyer型算子在紧圆盘对解析函数的等价定理.结果表明q-Bernstein-Durrmeyer型算子从实空间推广到复空间扩展了逼近性质. |
| 关键词: q-Bernstein-Durrmeyer算子 等价定理 Voronovskaja型定理 |
| DOI： |
| 分类号:O174.41 |
| 基金项目:内蒙古自治区自然科学基金青年项目(2023QN01004). |
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| EQUIVALENCE OF COMPLEX APPROXIMATION BY q-BERSTEIN-DURRMEYER OPERATOR IN COMPACT DISKS（0 ＜ q ＜ 1） |
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JIA Yi-xin,HAN Ling-xiong
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| Abstract: |
| This paper studies the relevant properties of the complex q-Bernstein-Durrmeyer type operators in the compact disk. By using the higher-order Cauchy integral formula, Taylor expansion and Bernstein inequality, the simultaneous approximation of the operator in the compact disk and the Voronovskaja-type theorem on the closed unit disk were obtained, and the equivalence theorem of the q-Bernstein-Durrmeyer type operator for analytic functions in the compact disk was given. The results show that the q-Bernstein-Durrmeyer type operator extends the approximation property from real space to complex space. |
| Key words: q-Bernstein-Durrmeyer operator Equivalence theorem Voronovskaja type results |
