移动紧圆盘上Bernstein-Durrmeyer型算子的逼近

数学物理学报 ›› 2020, Vol. 40 ›› Issue (3): 545-555.

• 论文 • 下一篇

移动紧圆盘上Bernstein-Durrmeyer型算子的逼近

庞兆鋆¹,虞旦盛^1,*(),周平²

¹ 杭州师范大学数学系杭州 310036
² Department of Mathematics, Statistics and Computer Science, St. Francis Xavier University, Antigonish, NS B2G 2W5, Canada

收稿日期:2019-05-15 出版日期:2020-06-26 发布日期:2020-07-15
通讯作者: 虞旦盛 E-mail:dsyu@hznu.edu.cn

On Approximation by Bernstein-Durrmeyer-Type Operators in Movable Compact Disks

Zhaojun Pang¹,Dansheng Yu^1,*(),Ping Zhou²

¹ Department of Mathematics, HangZhou Normal University, Hangzhou 310036
² Department of Mathematics, Statistics and Computer Science, St. Francis Xavier University, Antigonish, NS B2G 2W5, Canada

Received:2019-05-15 Online:2020-06-26 Published:2020-07-15
Contact: Dansheng Yu E-mail:dsyu@hznu.edu.cn

摘要/Abstract

摘要：

为了逼近移动圆盘上的解析函数，构造了一种新的Bernstein-Durrmeyer型算子，并给出其在移动圆盘上同时逼近的一致逼近速度估计.

关键词: 复Bernstein-Durrmeyer型算子, 可移动紧圆盘, 逼近估计

Abstract:

To approximate analytic functions in movable compact disks, we introduce a new kind of Bernstein-Durrmeyer-Type polynomials. The order of simultaneous approximation rate of the new polynomials in the movable compact disks is given.

Key words: Complex Bernstein-Durrmeyer type operators, Movable compact disks, Approximation rates

中图分类号:

O174

庞兆鋆,虞旦盛,周平. 移动紧圆盘上Bernstein-Durrmeyer型算子的逼近[J]. 数学物理学报, 2020, 40(3): 545-555.

Zhaojun Pang,Dansheng Yu,Ping Zhou. On Approximation by Bernstein-Durrmeyer-Type Operators in Movable Compact Disks[J]. Acta mathematica scientia,Series A, 2020, 40(3): 545-555.

参考文献

1	Gal S G . Approximation by complex genuine Durrmeyer type polynomials in compact disks. Appl Math Comput, 2010, 217, 1913- 1920
2	Gal S G . Approximation by Complex Bernstein and Convolution Type Operstors. Singapore:World Scientific, 2009
3	Gal S G . Overconvergence in Complex Approximation. New York:Springer, 2013
4	Gal S G . Voronovskaja's theorem and iterations for complex Bernstein polynomials in compact disks. Mediterr Math J, 2008, 5, 253- 272
5	Gal S G . Approximation by complex Bernstein-Kantorovich and Stancu-Kanrorovich polynomials and their iterates in compact disks. Appl Math Comput, 2009, 58, 734- 743
6	Gal S G . Approximation by complex Bernstein-Durrmeyer polynomials with jacobi weights in compact disks. Math Balk, 2010, 24, 103- 110
7	Gal S G , Gupta V . Approximation by a Durrmeyer-Stancu-type operator in compact disks. Ann Univ Ferrara, 2011, 57, 261- 274
8	Gal S G , Gupta V . Approximation by complex Lupas-Durrmeyer polynomials based on Polya distribution. Banach J Math Anal, 2016, 10, 209- 221
9	Gupta V . Approximation properties by Bernstein-Durrmeyer type operators. Complex Anal Oper Theory, 2013, 7, 363- 374
10	Gupta V . Direct estimates for a new general family of Durrmeyer type operators. Bollettino dell'Unione Matematica Italiana, 2015, 7, 279- 288
11	Gupta V , Agarwal R P . Convergence Estimates in Approximation Theory. Switzerland:Springer, 2014
12	Gupta V . On approximation properties of a new type Bernstein-Durrmeyer operators. Math Slovaca, 2015, 65, 1107- 1122
13	Mahmudov N I . Approximation by Bernstein-Durrmeyer-type operators in compact disks. Appl Math Letter, 2011, 24, 1231- 1238
14	Mahmudov N I . Approximation by genuine q-Bernstein-Durrmeyer polynomials in compact disks. Hacet J Math Stat, 2011, 40, 77- 89
15	Mahmudov N I , Gupta V . Approximation by genuine Durrmeyer-Stancu polynomials in compact disks. Math Comput Modelling, 2012, 55, 278- 285
16	Lorentz G G . Bernstein Polynomials. 2nd edn. New York: Chelsea, 1986
17	Jiang B , Yu D S . On Approximation by Bernstein-Stancu polynomials in movable compact disks. Result Math, 2017, 72, 1535- 1543
18	Jiang B, Yu D S. Approximation by Durrmeyer type Bernstein-Stancu polynomials in movable compact disks. Result Math, 2019, 74: Article 28
19	Jiang B , Yu D S . On approximation by Stancu type Bernstein-Schurer polynomials in compact disks. Result Math, 2017, 72, 1623- 1638
20	Ren M Y, Zeng X M. Approximation by a kind of complex modified q-Durrmeyer type operators in compact disks. J Inequal Appl, 2012, 2012: Article 212
21	Ren M Y, Zeng X M, Zeng L. Approximation by complex Durrmeyer-Stancu type operators in compact disks. J Inequal Appl, 2013, 2012: Article 442

[1]	胡浩, 叶善力. Hilbert 矩阵算子在对数加权 Bergman 空间上的范数[J]. 数学物理学报, 2025, 45(5): 1405-1416.
[2]	万沪龙, 刘慧芳. 某类非线性微分差分方程亚纯解的结构[J]. 数学物理学报, 2025, 45(5): 1577-1585.
[3]	冀蕾, 魏明权, 燕敦验. Hardy 型算子的交换子在中心 Morrey 空间上的弱有界性刻画[J]. 数学物理学报, 2025, 45(4): 1013-1022.
[4]	吕军. 平面具有四元数字集自相似测度的谱结构研究[J]. 数学物理学报, 2025, 45(4): 1023-1040.
[5]	温新奇, 袁程. Hardy空间 $H^1(\mathbb{B}_{n})$ 上的 Toeplitz 型算子[J]. 数学物理学报, 2025, 45(4): 1161-1170.
[6]	邵旭馗, 王素萍, 陶双平. 非齐次变指标 Herz-Morrey-Hardy 空间上的变量核 Marcinkiewicz 积分及其交换子[J]. 数学物理学报, 2025, 45(3): 653-664.
[7]	李子燕, 陶祥兴. 基于小波基的乘积加权 Besov 空间和乘积加权 Triebel-Lizorkin 空间的 Plancherel-Pôlya 型刻画[J]. 数学物理学报, 2025, 45(3): 665-686.
[8]	刘红梅, 李阳. 两类Kampé de Fériet,级数的简化和求和公式[J]. 数学物理学报, 2025, 45(1): 136-152.
[9]	胡可奇, 张庆彩. 拟周期函数的性质及其应用[J]. 数学物理学报, 2024, 44(6): 1415-1425.
[10]	张杰, 孙艺铭, 刘永平. 加权 Korobov 空间中多元 $\mathbb{L}_{\infty}$-逼近问题的指数收敛易处理性[J]. 数学物理学报, 2024, 44(3): 525-538.
[11]	王瑶瑶, 吕玫钏, 李文明. 高维 Hardy 算子及其交换子的双权不等式[J]. 数学物理学报, 2024, 44(3): 539-546.
[12]	刘华, Basma Al-Shutnawi. 全纯系数形式幂级数的收敛集[J]. 数学物理学报, 2024, 44(3): 563-574.
[13]	孙小春, 吴育联, 徐郜婷. 分数阶不可压缩 Navier-Stokes-Coriolis 方程解的整体适定性[J]. 数学物理学报, 2024, 44(3): 737-745.
[14]	库福立. 多线性 Calderón-Zygmund 算子的交换子在广义 Morrey 空间上的紧性[J]. 数学物理学报, 2024, 44(2): 286-297.
[15]	程鑫, 张婧. 单边算子的多线性交换子在 Triebel-Lizorkin 空间上的加权有界性[J]. 数学物理学报, 2024, 44(1): 50-59.

移动紧圆盘上Bernstein-Durrmeyer型算子的逼近

On Approximation by Bernstein-Durrmeyer-Type Operators in Movable Compact Disks

RichHTML

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0