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

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	635-644
Number of pages	10
Journal	Mathematica Slovaca
Volume	61
Issue number	4
DOIs	https://doi.org/10.2478/s12175-011-0033-2
State	Published - Aug 2011

Bibliographical note

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).

Keywords

Meyer-König and Zeller operators
absolute moment
absolutely continuous functions
approximation

ASJC Scopus subject areas

General Mathematics

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10.2478/s12175-011-0033-2

Cite this

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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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AU - Cheng, Fuhua (Frank)

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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