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Approximation of Functions by Polynomials in C[-L, 1]

Published online by Cambridge University Press:  20 November 2018

Z. Ditzian  and
D. Jiang
Z. Ditzian
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta
D. Jiang
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta
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Abstract

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A pointwise estimate for the rate of approximation by polynomials , For 0 ≤ ƛ ≤ 1, integer r, and δn(x) = n-1 + φ(x), is achieved here. This formula bridges the gap between the classical estimate mentioned in most texts on approximation and obtained by Timan and others (ƛ = 0) and the recently developed estimate by Totik and first author (ƛ = 1 ). Furthermore, a matching converse result and estimates on derivatives of the approximating polynomials and their rate of approximation are derived. These results also cover the range between the classical pointwise results and the modern norm estimates for C[— 1,1].

Keywords

41A2541A27Polynomial approximationdirect and converse results
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 5 , 01 October 1992 , pp. 924 - 940
Copyright
Copyright © Canadian Mathematical Society 1992

References

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