On the rate of convergence for the Chebyshev series

Kamel Al-Khaled

doi:10.35834/2002/1401004

On the rate of convergence for the Chebyshev series

Kamel Al-Khaled^*

^*Corresponding author for this work

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

2 Citations (Scopus)

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 S_n(f;x) to f(x) in terms of the modulus of continuity of the total variation of f(x).

Original language	English
Pages (from-to)	4-10
Number of pages	7
Journal	Missouri Journal of Mathematical Sciences
Volume	14
Issue number	1
DOIs	https://doi.org/10.35834/2002/1401004
Publication status	Published - 2002
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.35834/2002/1401004

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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).",

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AB - 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).

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On the rate of convergence for the Chebyshev series

Abstract

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