Pointwise estimates for the derivative of algebraic polynomials

2021/04/02 by Adrian Savchuk, Savchuk, Adrian
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Approximation Theory and Sequence Spaces #Complex Variables (math.CV) #FOS: Mathematics #Mathematical functions and polynomials #math.CV

paper · pdf · doi:10.48550/arxiv.2104.01248

arxiv created 2021/04/02 · openalex publication_date 2021/04/02 · arxiv updated 2021/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We give the sufficient condition on coefficients a_k of an algebraic polynomial P(z)=∑_k=0ⁿa_kz^k, a_n\not=0, for the pointwise Bernstein inequality |P'(z)|≤ n|P(z)| to be true for all z∈\mathbb D:=\w∈\mathbb C : |w|≤ 1\.

Related

• Certain Bernstein-type L_p inequalities for polynomials
• On Visser's inequality concerning coefficient estimates for a polynomial
• V. Markov's problem for monotone polynomials
• Bernstein- and Markov-type inequalities
• Arestov's theorems on Bernstein's inequality