### 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 |
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Pages (from-to) | 1-7 |

Number of pages | 7 |

Journal | Missouri Journal of Mathematical Sciences |

Volume | 14 |

Issue number | 1 |

Publication status | Published - 2002 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Missouri Journal of Mathematical Sciences*,

*14*(1), 1-7.

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

Research output: Contribution to journal › Article

*Missouri Journal of Mathematical Sciences*, vol. 14, no. 1, pp. 1-7.

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TY - JOUR

T1 - On the rate of convergence for the Chebyshev series

AU - Al-Khaled, Kamel

PY - 2002

Y1 - 2002

N2 - 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).

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).

UR - http://www.scopus.com/inward/record.url?scp=17844402219&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=17844402219&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:17844402219

VL - 14

SP - 1

EP - 7

JO - Missouri Journal of Mathematical Sciences

JF - Missouri Journal of Mathematical Sciences

SN - 0899-6180

IS - 1

ER -