A refinement of an inequality of S. Bernstein. (English) Zbl 0691.30007

Let p(z) be a polynomial of degree n. Recently, C. Frappier, Q. I. Rahman and S. Ruscheweyh [Trans. Am. Math. Soc. 288, 69-99 (1985; Zbl 0567.30006)] have shown that \[ (*)\quad_{| z| =1}| p'(z)| \leq n_{1\leq k\leq 2n}| p(e^{ik\pi /n})|. \] In the paper under review, the author shows that the bound in (*) can be considerably improved. In addition, the author obtains a sharp lower bound for the maximum of \(| p'(z)|\) on \(| z| =1\).
Reviewer: G.Csordas


30C10 Polynomials and rational functions of one complex variable


Zbl 0567.30006
Full Text: DOI


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