On the rate of convergence for the Chebyshev series

Kamel Al-Khaled

Research output: Contribution to journalArticle

Abstract

Let f(x) be a function of bounded variation on [-1,1] and S n(f;x) the nth partial sum of the expansion of f(x) in a Chebyshev series of the second kind. In this note we give the estimate for the rate of convergence of the sequence Sn(f;x) to f(x) in terms of the modulus of continuity of the total variation of f(x).

Original languageEnglish
Pages (from-to)1-7
Number of pages7
JournalMissouri Journal of Mathematical Sciences
Volume14
Issue number1
Publication statusPublished - 2002

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Chebyshev Series
Functions of Bounded Variation
Modulus of Continuity
Total Variation
Partial Sums
Rate of Convergence
Estimate

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On the rate of convergence for the Chebyshev series. / Al-Khaled, Kamel.

In: Missouri Journal of Mathematical Sciences, Vol. 14, No. 1, 2002, p. 1-7.

Research output: Contribution to journalArticle

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