Far Eastern Mathematical Journal

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On the distortion theorems for algebraic polynomials

V. N. Dubinin

2011, issue 1, Ñ. 28–36

The applications of a boundary Schwarz lemma and the properties of the condenser capacity to some inequalities for polynomials and their derivatives are considered. We prove a new Bernstein-type inequality for the polynomials on a circle, two-sided estimates for the polynomials with constraints on their critical values, and two-sided estimates of the average distortion computed at zeros of the polynomials.

polynomials, critical points, critical values, Chebyshev polynomial, Bernstein-type inequality, distortion theorem, condenser capacity

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