A refinement of an inequality of S. Bernstein
Let p(z) be a polynomial of degree n. Recently, \textit{C. Frappier}, \textit{Q. I. Rahman} and \textit{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 \(| z| =1\).
scientific article; zbMATH DE number 4130716