Geodesic
Conformal mappings and inequalities for algebraic polynomials.~II
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 19, Tome 302 (2003), pp. 18-37

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This paper supplements the previous paper of the author under the same title. An analog of the Schwarz boundary lemma is proved for non-univalent regular mappings of subsets of the unit disk onto a disk. Based on this result, certain strengthened inequalities of Bernstein type for algebraic polynomials are obtained. The generalized Mendeleev problem is discussed. Two-sided bounds for the module of the derivative of a polynomial with critical points on an interval are established. Bounds for the coefficients of polynomials under certain constraints are provided. 
@article{ZNSL_2003_302_a1,
     author = {V. N. Dubinin},
     title = {Conformal mappings and inequalities for algebraic {polynomials.~II}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {18--37},
     publisher = {mathdoc},
     volume = {302},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_302_a1/}
}
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V. N. Dubinin. Conformal mappings and inequalities for algebraic polynomials.~II. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 19, Tome 302 (2003), pp. 18-37. http://geodesic.mathdoc.fr/item/ZNSL_2003_302_a1/