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

Xiao Ming Zeng, Fuhua (Frank) Cheng

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)635-644
Number of pages10
JournalMathematica Slovaca
Volume61
Issue number4
DOIs
StatePublished - 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

  • Mathematics (all)

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