First order absolute moment of Meyer-König and Zeller operators and their approximation for some absolutely continuous functions

Xiao Ming Zeng; Fuhua (Frank) Cheng

doi:10.2478/s12175-011-0033-2

First order absolute moment of Meyer-König and Zeller operators and their approximation for some absolutely continuous functions

Xiao Ming Zeng
, Fuhua (Frank) Cheng

Computer Science

Producción científica: Article › revisión exhaustiva

3 Citas (Scopus)

Resumen

A sharp estimate is given for the first order absolute moment of Meyer-König and Zeller operators M_n. This estimate is then used to prove convergence of approximation of a class of absolutely continuous functions by the operators M_n. The condition considered here is weaker than the condition considered in a previous paper and the rate of convergence we obtain is asymptotically the best possible.

Idioma original	English
Páginas (desde-hasta)	635-644
Número de páginas	10
Publicación	Mathematica Slovaca
Volumen	61
N.º	4
DOI	https://doi.org/10.2478/s12175-011-0033-2
Estado	Published - ago 2011

Nota bibliográfica

Funding Information:
2010 M a t h e m a t i c s Subj ect C l assi f i cati on: Primary 41A36, 41A25, 41A10. Keywords: absolute moment, Meyer-König and Zeller operators, approximation, absolutely continuous functions. This work is supported by China, the Natural Science Foundation of Fujian Province (Grant No. 2010J01012), the National Defense Basic Scientific Research program of China (Grant No. B1420110155) and the Science and Technology Foundation of Xiamen City of China (Grant No. 20083012).

Financiación

2010 M a t h e m a t i c s Subj ect C l assi f i cati on: Primary 41A36, 41A25, 41A10. Keywords: absolute moment, Meyer-König and Zeller operators, approximation, absolutely continuous functions. This work is supported by China, the Natural Science Foundation of Fujian Province (Grant No. 2010J01012), the National Defense Basic Scientific Research program of China (Grant No. B1420110155) and the Science and Technology Foundation of Xiamen City of China (Grant No. 20083012).

Financiadores	Número del financiador
Science and Technology Foundation of Xiamen City of China	20083012
Natural Science Foundation of Fujian Province	2010J01012
National Defense Basic Scientific Research Program of China	B1420110155

ASJC Scopus subject areas

General Mathematics

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10.2478/s12175-011-0033-2

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abstract = "A sharp estimate is given for the first order absolute moment of Meyer-K{\"o}nig and Zeller operators Mn. This estimate is then used to prove convergence of approximation of a class of absolutely continuous functions by the operators Mn. The condition considered here is weaker than the condition considered in a previous paper and the rate of convergence we obtain is asymptotically the best possible.",

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N2 - A sharp estimate is given for the first order absolute moment of Meyer-König and Zeller operators Mn. This estimate is then used to prove convergence of approximation of a class of absolutely continuous functions by the operators Mn. The condition considered here is weaker than the condition considered in a previous paper and the rate of convergence we obtain is asymptotically the best possible.

AB - A sharp estimate is given for the first order absolute moment of Meyer-König and Zeller operators Mn. This estimate is then used to prove convergence of approximation of a class of absolutely continuous functions by the operators Mn. The condition considered here is weaker than the condition considered in a previous paper and the rate of convergence we obtain is asymptotically the best possible.

KW - Meyer-König and Zeller operators

KW - absolute moment

KW - absolutely continuous functions

KW - approximation

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JO - Mathematica Slovaca

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First order absolute moment of Meyer-König and Zeller operators and their approximation for some absolutely continuous functions

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

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