Point-wise estimates for the derivative of algebraic polynomials

A. V. Savchuk

doi:10.30970/ms.56.2.208-211

A. V. Savchuk Taras Shevchenko National University of Kyiv

DOI: https://doi.org/10.30970/ms.56.2.208-211

Keywords: algebraic polynomial; logarithmic derivative; Bernstein’s inequality

Abstract

We give a sufficient condition on coefficients $a_k$ of an algebraic polynomial $P(z)=\sum\limits_{k=0}^{n}a_kz^k$, $a_n\not=0,$ such that the pointwise Bernstein inequality $|P'(z)|\le n|P(z)|$ is true for all $z,\ |z|\le 1$.

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