一类Stancu型的Sz′asz-Mirakjan-Durrmeyer算子的逼近性质研究
On the approximation properties of a class of Stancu-type Sz′asz-Mirakjan-Durrmeyer operators
连博勇 1蔡清波2
作者信息
- 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
- 折叠
摘要
该文介绍了一类Stancu型的Sz´asz-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.
Abstract
In this paper,a class of Sz´asz-Mirakjan-Durrmeyer operators of Stancu type are introduced,and the first 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
Sz´asz-Mirakjan-Durrmeyer算子/K-泛函/连续模/Voronvskaya型渐近展开公式Key words
Sz´asz-Mirakjan-Durrmeyer operators/K-functional/Modulus of continuity/Voronovskaya-type asymptotic formula引用本文复制引用
基金项目
福建省自然科学基金(2020J01783)
仰恩大学学科带头人专项()
出版年
2024
NETL
NSTL
万方数据