Bézier Durrmeyer型λ-Bernstein算子的收敛阶  

Rate of convergence of Bézier Durrmeyer type λ-Bernstein operators

作　　者：蔡清波[1] 陈淑铌 CAI Qingbo;CHEN Shuni(School of Mathematics and Computer Science,Quanzhou Normal University,Quanzhou 362000,China;School of Mathematical Sciences,Xiamen University,Xiamen 361005,China)

机构地区：[1]泉州师范学院数学与计算机科学学院,福建泉州362000 [2]厦门大学数学科学学院,福建厦门361005

出　　处：《厦门大学学报（自然科学版）》2019年第5期726-732,共7页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(11601266,61572020);福建省自然科学基金(2016J05017);福建省高等学校新世纪优秀人才支持计划;泉州市高层次人才创新创业项目(2018C087R)

摘　　要：引入了带参数λ∈[-1,1]的Bézier Durrmeyer型λ-Bernstein算子D(α)n,λ(f;x),建立了一个基于二阶连续模的整体逼近定理及一个由Ditzian-Totik光滑模导出的直接逼近定理.同时结合Bojanic-Cheng分解方法及若干分析技巧导出了一个D(α)n,λ(f;x)对一类绝对连续函数收敛阶的渐近估计.最后,对于某给定的函数f,给出一个例子说明了Dn,λ^(α)(f;x)对f(x)的收敛性.In this paper,we introduce Bézier Durrmeyer typeλ-Bernstein operators D(α)n,λ(f;x)with a parameterλ∈[-1,1].We establish a global approximation theorem in terms of the second-order modulus of continuity and a direct approximation theorem by means of the Ditzian-Totik modulus of smoothness.We also combine the Bojanic-Cheng s decomposition method jointly with some analysis techniques to derive an asymptotically estimate on the rate of convergence for some absolutely continuous functions of D(α)n,λ(f;x).Finally,we present an example to show the convergence of Dn,λ^(α)(f;x)to f(x)with some given f.

关 键 词：λ-Bernstein算子 基函数 连续模 收敛阶 绝对连续函数 

分 类 号：O175.41[理学—数学]