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Zbl 0605.41026
Blatt, H.-P.; Saff, E.B.
Behavior of zeros of polynomials of near best approximation. (English)
[J] J. Approximation Theory 46, 323-344 (1986). ISSN 0021-9045

The purpose of this paper is to study the asymptotic behaviour of the zeros of polynomials of near best approximation to continuous functions f on a compact set E in the case when f is analytic on the interior of E but not everywhere on the boundary. For example suppose E is a finite union of compact intervals of the real line and f is a continuous function on E, but is not analytic on E, then the authors show that every point of E is a limit point of zeros of the polynomials of best uniform approximation to f on E. This fact answers a question posed by {\it P. B. Borwein} [Approximation theory IV, Proc. int. Conf., Tex. A \& M Univ. 1983, 365-368 (1983; Zbl 0555.41021)].
[S.M.Mazhar]

MSC 2000:: *41A50 Best approximation
30C15 Zeros of polynomials, etc. (one complex variable)
30E10 Approximation in the complex domain

Keywords: near best approximation; zeros of the polynomials of best uniform approximation

Citations: Zbl 0555.41021

Cited in: Zbl 0943.41013 Zbl 0767.41032

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