Open AccessPoint-wise estimates for the derivative of algebraic polynomials
Author(s) -
Adrian Savchuk
Publication year - 2021
Publication title -
matematičnì studìï/matematičnì studìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.482
H-Index - 8
eISSN - 2411-0620
pISSN - 1027-4634
DOI - 10.30970/ms.56.2.208-211
Subject(s) - pointwise , mathematics , algebraic number , polynomial , derivative (finance) , combinatorics , bernstein polynomial , pure mathematics , discrete mathematics , mathematical analysis , financial economics , economics
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 $z,\ |z|\le 1$.