[1]连博勇,蔡清波.一类λ型的Bernstein算子列的逼近性质[J].泉州师范学院学报,2019,(02):35-38.
 LIAN Boyong,CAI Qingbo.On the Rate of Convergence of a New Family of λ Type Bernstein Operators[J].,2019,(02):35-38.
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一类λ型的Bernstein算子列的逼近性质()
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《泉州师范学院学报》[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2019年02期
页码:
35-38
栏目:
数学·计算科学
出版日期:
2019-04-15

文章信息/Info

Title:
On the Rate of Convergence of a New Family of λ Type Bernstein Operators
文章编号:
1009-8224(2019)02-0035-04
作者:
连博勇1蔡清波2
1.仰恩大学 数学系,福建 泉州 362014; 2.泉州师范学院 数学与计算机科学学院,福建 泉州 362000
Author(s):
LIAN Boyong1CAI Qingbo2
1.Department of Mathematics,Yang'en University,Fujian 362014,China; 2.College of Mathematics and Computer Science,Quanzhou Normal University,Fujian 362000,China
关键词:
Bernstein算子 收敛阶 有界变差函数
Keywords:
Bernstein operators rate of convergence bounded variation functions
分类号:
O174.41
文献标志码:
A
摘要:
根据经典的Bojanic-Cheng分解方法,结合分析技术,研究了一类新型的Bernstein算子列对一类导数为有界变差的函数类的逼近.首先由蔡清波关于一阶二阶矩的结论得到一阶中心绝对矩Bn,λ(|t-x|,x)的估计,接着估计了另外一项Bn,λ(∫txφx(u)du,x),最后得到该新型算子的收敛阶估计.
Abstract:
By using Bojanic-Cheng's method and analysis techniques,the authors studied the rate of convergence of a new family of Bernstein operators for some absolutely continuous functions with a derivative equivalent to a bounded variation.By the result of Cai qingbo about the operator's first moment and second moment,the authors obtained the first central absolute moment Bn,λ(|t-x|,x).Later,the other part Bn,λ(∫txφx(u)du,x)was estimated.Finally,the convergence rate of the new type operators was obtained.

参考文献/References:

[1] CAI Q B,LIAN B Y,ZHOU G.Approximation properties of λ-Bernstein operators [J].Journal of Inequalities and Applications,2018,61.https://doi.org/10.1186/s13660-018-1653-7.
[2] BOJANIC R,CHENG F.Rate of convergence of Bernstein polynomials for functions with derivatives of bounded variation [J].Journal of Mathematical Analysis and Applications,1989,141(1):136-151.
[3] ZENG X M,CHEN X J.Approximation for bounded functions and absolutely continuous functions by Beta operators [J].Computers & Mathematics with Applications,2006,51(9):1585-1592.
[4] 连博勇,蔡清波.关于Bernstein-Kantorovich-Bézier算子对一类绝对连续函数的逼近[J].泉州师范学院学报,2008,26(4):7-9.
[5] GUPTA V,SOYBA S D.Convergence of integral operator based on different distributions [J].Filomat,2016,30(8):2277-2287.
[6] GUPTA V,ACU A M,SOFONEA D F.Approximation of Baskakov type Polya-Durrmeyer operators [J].Applied Mathematics and Computation,2017,294:318-331.

相似文献/References:

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 LIAN Bo-yong,CAI Qing-bo.An Estimate on the Convergence of Bezier Variantof Bleimann-Butzer and Hahn Operators[J].,2013,(02):8.
[2]黄东兰,王平华.Durrmeyer-Bzier算子收敛阶的新估计[J].泉州师范学院学报,2014,(06):86.
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备注/Memo

备注/Memo:
收稿日期:2018-09-06
作者简介:连博勇(1982-),男,福建泉州人,副教授,主要从事函数逼近论与计算几何研究.
基金项目:国家自然科学基金项目(11601266); 福建省自然科学基金项目(2006J05017); 福建省高校杰出青年科研人才培育计划(2016)
更新日期/Last Update: 2019-04-15