On the approximation properties of Cesàro means of negative order of Walsh-Fourier series

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44 Citations (Scopus)

Abstract

In this paper we establish approximation properties of Cesàro (C, -α)-means with α ε (0, 1) of Walsh-Fourier series. This result allows one to obtain the condition which is sufficient for the convergence of the means σn (f, x) to f (x) in the Lp-metric. We also show that this condition cannot be improved in the case p = 1.

Original languageEnglish
Pages (from-to)9-20
Number of pages12
JournalJournal of Approximation Theory
Volume115
Issue number1
DOIs
Publication statusPublished - 2002
Externally publishedYes

Keywords

  • Approximation
  • Cesàro means
  • Walsh functions

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • General Mathematics
  • Applied Mathematics

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