一类Stancu型的Szász-Mirakjan-Durrmeyer算子的逼近性质研究  

On the approximation properties of a class of Stancu-type Szász-Mirakjan-Durrmeyer operators

作　　者：连博勇[1] 蔡清波[2] LIAN Bo-yong;CAI Qing-bo(Dept.of Math.,Yang-En Univ.,Quanzhou 362014,China;School of Math.and Comput.Sci.,Quanzhou Normal Univ.,Quanzhou 362000,China)

机构地区：[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

出　　处：《高校应用数学学报（A辑）》2024年第2期211-217,共7页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：福建省自然科学基金(2020J01783);仰恩大学学科带头人专项资助。

摘　　要：该文介绍了一类Stancu型的Szász-Mirakjan-Durrmeyer算子,计算了该算子的一阶到四阶矩.然后用连续模和K-泛函等工具,讨论了该算子的逼近性质,还研究了算子对Lipschitz函数类的估计.最后建立了该算子的Voronvskaya型渐近展开式.所得定理扩展了Aslan(2022)的结果.In this paper,a class of Szász-Mirakjan-Durrmeyer operators of Stancu type are introduced,and thefirst to fourth order moments of the operators are calculated.Next,with tools such as modulus of continuity and K-functional,the approximation properties of the operators are discussed.The estimation of the Lipschitz function class by the operators is also studied.Finally,the Voronvskaya type asymptotic expansion of the operators is established.The theorems extend the results of Aslan(2022).

关 键 词：Szász-Mirakjan-Durrmeyer算子 K-泛函 连续模 Voronvskaya型渐近展开公式 

分 类 号：O174.41[理学—数学]