Geodesic
On the distortion theorems for algebraic polynomials
Dalʹnevostočnyj matematičeskij žurnal, Tome 11 (2011) no. 1, pp. 28-36

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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. 
@article{DVMG_2011_11_1_a2,
     author = {V. N. Dubinin},
     title = {On the distortion theorems for algebraic polynomials},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {28--36},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2011_11_1_a2/}
}
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V. N. Dubinin. On the distortion theorems for algebraic polynomials. Dalʹnevostočnyj matematičeskij žurnal, Tome 11 (2011) no. 1, pp. 28-36. http://geodesic.mathdoc.fr/item/DVMG_2011_11_1_a2/