Inequalities for the maximum modulus of univariate constrained polynomials

Some Inequalities concerning Derivative and Maximum Modulus of Polynomials

In this paper, we prove some compact generalizations of some well-known Bernstein type inequalities concerning the maximum modulus of a polynomial and its derivative in terms of maximum modulus of a polynomial on the unit circle. Besides, an inequality for self-inversive polynomials has also been obtained, which in particular gives some known inequalities for this class of polynomials. All the ...

On the Maximum Modulus of Polynomials. Ii

Let f(z) := ∑n ν=0 aνz ν be a polynomial of degree n having no zeros in the open unit disc, and suppose that max|z|=1 |f(z)| = 1. How small can max|z|=ρ |f(z)| be for any ρ ∈ [0 , 1)? This problem was considered and solved by Rivlin [4]. There are reasons to consider the same problem under the additional assumption that f ′(0) = 0. This was initiated by Govil [2] and followed up by the present ...

Some Inequalities for Maximum Modules of Polynomials

A well-known result of Ankeney and Rivlin states that if p(z) is a polynomial of degree n, such that p(z) 0 in [z[ < 1, then maxlz[=R>_l Ip(z)l <_ (---)maxlzl= Ip(z)l. In this paper we 1)rove ,some generalizations and refinements of this result.

Markov-type Inequalities for Constrained Polynomials

Bernstein Inequalities for Polynomials with Constrained Roots

We prove Bernstein type inequalities for algebraic polynomials on the finite interval I := [−1, 1] and for trigonometric polynomials on R when the roots of the polynomials are outside of a certain domain of the complex plane. The case of real vs. complex coefficients are handled separately. In case of trigonometric polynomials with real coefficients and root restriction, the Lpsituation will al...