Rates of convergence for Jakimovski-Leviatan operators in terms of the Ditzian-Totikmodulus

被引：1
|
作者：
Acu, Ana-Maria [1 ]
Adell, Jose A. [2 ]
Rasa, Ioan [3 ]
机构：
[1] Lucian Blaga Univ Sibiu, Dept Math & Informat, Str Dr I Ratiu, Sibiu 550012, Romania
[2] Univ Zaragoza, Dept Metodos Estadist, Zaragoza 50009, Spain
[3] Tech Univ Cluj Napoca, Dept Math, Str Memorandumului 28, Cluj Napoca 400114, Romania
来源：
BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2023年 / 17卷 / 04期
关键词：
Jakimovski-Leviatan operators; Poisson distribution; Ditzian-Totik modulus; Appell sequence; Touchard polynomials; APPROXIMATION;
D O I：
10.1007/s43037-023-00281-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We obtain uniform convergence results for the Jakimovski-Leviatan operators Psi(n) in terms of the Ditzian-Totik modulus, providing at the same time explicit upper constants. A main ingredient of the proof is the representation of such operators as an infinite linear combination of Szasz-Mirakyan operators. Closed-form expressions for the moments of Psi(n) involving the Touchard polynomials are given. Specific examples of the Appell sequences defining Psi(n) are also discussed.
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页数：16
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