广义含参Bernstein-Kantorovich算子的逼近性质  

Approximation Properties of Generalized ParametricBernstein-Kantorovich Operators

作　　者：刘玉洁 程文韬 汪洋 杨瑞 LIU Yu-jie;CHENG Wen-tao;WANG Yang;YANG Rui(School of Mathematics and Physics,Anqing Normal University,AnqingAnhui 246133,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《辽宁工业大学学报（自然科学版）》2023年第6期404-409,共6页Journal of Liaoning University of Technology(Natural Science Edition)

基　　金：国家自然科学基金项目(11626031);安徽省自然科学基金项目(1908085QA29);安徽省高校自然科学研究重点项目(KJ2021A0648,KJ2019A0572)。

摘　　要：通过引入可调参数,在带有Pochhammerk符号的Lupas算子的基础上,构建了一种广义的Bernstein-Kantorovich算子。首先给出该算子的各阶原点矩和中心矩渐近公式,利用经典的一阶、二阶光滑模和其Peetre’K-泛函等工具估计该新算子的收敛速度;其次,建立了该算子的Voronovskaya型定理。By introducing adjustable parameters,a generalized Bernstein-Kantorovich operator is constructed on the basis of Lupaşwith Pochhammer k symbol.Firstly,the asymptotic formulas of the origin moment and central moment of the new operator are given.The convergence rate of the new operator is estimated by using the classical first-order and second-order modulus of smoothness and its Peetre’K-functional tools.Secondly,the Voronovskaya type theorem of the operator is established.

关 键 词：Lupa?-Beta算子 Pochhammer k符号 收敛速度 Voronovskaya定理 

分 类 号：O174.41[理学—数学]