Complete Asymptotic Expansion for Generalized Favard Operators

被引：8
|
作者：
Abel, Ulrich [2 ]
Butzer, Paul L. [1 ]
机构：
[1] Rhein Westfal TH Aachen, Lehrstuhl Math, D-52056 Aachen, Germany
[2] Tech Hsch Mittelhessen, Fachbereich MND, D-61169 Friedberg, Germany
来源：
CONSTRUCTIVE APPROXIMATION | 2012年 / 35卷 / 01期
关键词：
Approximation by positive operators; Rate of convergence; Degree of approximation; Simultaneous approximation; Asymptotic expansions; APPROXIMATION;
D O I：
10.1007/s00365-011-9134-y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In the present paper we consider a generalization F(n,)sigma(n) of the Favard operators and study the local rate of convergence for smooth functions. As a main result we derive the complete asymptotic expansion for the sequence (F(n,)sigma(n) f)(x) as n tends to infinity. Furthermore, we consider a truncated version of these operators. Finally, all results were proved for simultaneous approximation.
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页码：73 / 88
页数：16
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