### Abstract

This paper is a generalization of the result obtained by F. Deutsch, G. Nürnberger, and I. Singer (1980, Pacific J. Math. 88, 9-31). It is shown that if Q is a locally compact totally ordered space, and N is an n-dimensional subspace of C_{0}(Q), then N is a weak Chebyshev subspace if and only if for each f ε{lunate} C_{0}(Q), there is g ε{lunate} N such that ∥f - g∥ = d(f, N) and (f - g) equioscillates at (n + 1) points.

Original language | English |
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Pages (from-to) | 129-141 |

Number of pages | 13 |

Journal | Journal of Approximation Theory |

Volume | 67 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1991 |

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### ASJC Scopus subject areas

- Analysis
- Numerical Analysis
- Mathematics(all)
- Applied Mathematics

### Cite this

**On weak Chebyshev subspaces. I. Equioscillation of the error in approximation.** / Kamal, Aref.

Research output: Contribution to journal › Article

*Journal of Approximation Theory*, vol. 67, no. 2, pp. 129-141. https://doi.org/10.1016/0021-9045(91)90013-Z

}

TY - JOUR

T1 - On weak Chebyshev subspaces. I. Equioscillation of the error in approximation

AU - Kamal, Aref

PY - 1991

Y1 - 1991

N2 - This paper is a generalization of the result obtained by F. Deutsch, G. Nürnberger, and I. Singer (1980, Pacific J. Math. 88, 9-31). It is shown that if Q is a locally compact totally ordered space, and N is an n-dimensional subspace of C0(Q), then N is a weak Chebyshev subspace if and only if for each f ε{lunate} C0(Q), there is g ε{lunate} N such that ∥f - g∥ = d(f, N) and (f - g) equioscillates at (n + 1) points.

AB - This paper is a generalization of the result obtained by F. Deutsch, G. Nürnberger, and I. Singer (1980, Pacific J. Math. 88, 9-31). It is shown that if Q is a locally compact totally ordered space, and N is an n-dimensional subspace of C0(Q), then N is a weak Chebyshev subspace if and only if for each f ε{lunate} C0(Q), there is g ε{lunate} N such that ∥f - g∥ = d(f, N) and (f - g) equioscillates at (n + 1) points.

UR - http://www.scopus.com/inward/record.url?scp=5844337915&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=5844337915&partnerID=8YFLogxK

U2 - 10.1016/0021-9045(91)90013-Z

DO - 10.1016/0021-9045(91)90013-Z

M3 - Article

VL - 67

SP - 129

EP - 141

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

SN - 0021-9045

IS - 2

ER -