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

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 con...

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Bibliographic Details
Published in:Mathematica Slovaca 2011-08, Vol.61 (4), p.635-644
Main Authors: Zeng, Xiao-Ming, Cheng, Fuhua (Frank)
Format: Article
Language:English
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Summary: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.
ISSN:0139-9918
1337-2211
DOI:10.2478/s12175-011-0033-2