Add to ORKGAbstract. Let D be the unit disk in the complex plane C and ‖p ‖: = max z∈∂D |p(z)|, where p(z) = ∑n k=0 ak(p)z k is a polynomial of degree at most n and ak(p) ∈ C. The following sharpening of Bernstein’s inequality ‖p′‖+ 2n n+ 2 |a0(p) | ≤ n‖p‖ has been proved by Ruscheweyh. Our main contribution concerns the case of equality which has remained unsolved since 1982. We prove another inequality of Bernstein type that leads to an improvement of the upper bound for ‖p′‖ under some additional condition
In an answer to a question raised by chemist Mendeleev, A. Markov proved that if is a real polynom...
If P(z) is a polynomial of degree n, having no zeros in the unit disc, then for all α, β ∈ C with α ...
If P(z) is a polynomial of degree n, having no zeros in the unit disc, then for all α, β ∈ C with α ...
Let D be the unit disc in the complex plane C and ‖ p ‖: = max z∈∂D | p(z) |, where p(z):= ∑n k=0 a...
AbstractLet D be the unit disk in the complex plane C. We prove that for any polynomial p of degree ...
The well known Bernstein Inequallty states that if D is a disk centered at the origin with radius R ...
AbstractBernstein's classical theorem states that for a polynomialPof degree at mostn, max|z|=1|P′(z...
Let D denote the unit disc of the complex plane and Pn the class of polynomials of degree at most n ...
AbstractLet pn(z) = an Πv = 1n (z − zv), an ≠ 0 be a polynomial of degree n and let ∥pn∥ = max¦z¦ = ...
Bernstein\u27s classical theorem states that for a polynomialPof degree at mostn, maxz=1P′(z)≤nmaxz=...
Bernstein\u27s classical theorem states that for a polynomialPof degree at mostn, maxz=1P′(z)≤nmaxz=...
It is known that for any polynomial p of degree less or equal to n, max |z|≤1 |p′(z) | ≤ n ma
AbstractLet P(z) be a polynomial of degree n and P′(z) its derivative. Using a recently developed in...
Let D denote the unit disc of the complex plane and Pn the class of polynomials of degree at most n ...
Abstract. Sharp extensions of some classical polynomial inequalities of Bernstein are established fo...
In an answer to a question raised by chemist Mendeleev, A. Markov proved that if is a real polynom...
If P(z) is a polynomial of degree n, having no zeros in the unit disc, then for all α, β ∈ C with α ...
If P(z) is a polynomial of degree n, having no zeros in the unit disc, then for all α, β ∈ C with α ...
Let D be the unit disc in the complex plane C and ‖ p ‖: = max z∈∂D | p(z) |, where p(z):= ∑n k=0 a...
AbstractLet D be the unit disk in the complex plane C. We prove that for any polynomial p of degree ...
The well known Bernstein Inequallty states that if D is a disk centered at the origin with radius R ...
AbstractBernstein's classical theorem states that for a polynomialPof degree at mostn, max|z|=1|P′(z...
Let D denote the unit disc of the complex plane and Pn the class of polynomials of degree at most n ...
AbstractLet pn(z) = an Πv = 1n (z − zv), an ≠ 0 be a polynomial of degree n and let ∥pn∥ = max¦z¦ = ...
Bernstein\u27s classical theorem states that for a polynomialPof degree at mostn, maxz=1P′(z)≤nmaxz=...
Bernstein\u27s classical theorem states that for a polynomialPof degree at mostn, maxz=1P′(z)≤nmaxz=...
It is known that for any polynomial p of degree less or equal to n, max |z|≤1 |p′(z) | ≤ n ma
AbstractLet P(z) be a polynomial of degree n and P′(z) its derivative. Using a recently developed in...
Let D denote the unit disc of the complex plane and Pn the class of polynomials of degree at most n ...
Abstract. Sharp extensions of some classical polynomial inequalities of Bernstein are established fo...
In an answer to a question raised by chemist Mendeleev, A. Markov proved that if is a real polynom...
If P(z) is a polynomial of degree n, having no zeros in the unit disc, then for all α, β ∈ C with α ...
If P(z) is a polynomial of degree n, having no zeros in the unit disc, then for all α, β ∈ C with α ...