Geodesic
On an application of conformal maps to inequalities for rational functions
Izvestiya. Mathematics , Tome 66 (2002) no. 2, pp. 285-297

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Using classical properties of conformal maps, we get new exact inequalities for rational functions with prescribed poles. In particular, we prove a new Bernstein-type inequality, an inequality for Blaschke products and a theorem that generalizes the Turan inequality for polynomials. The estimates obtained strengthen some familiar inequalities of Videnskii and Rusak. They are also related to recent results of Borwein, Erdelyi, Li, Mohapatra, Rodriguez, Aziz and others. 
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     author = {V. N. Dubinin},
     title = {On an application of conformal maps to inequalities for rational functions},
     journal = {Izvestiya. Mathematics },
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     number = {2},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2002_66_2_a1/}
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V. N. Dubinin. On an application of conformal maps to inequalities for rational functions. Izvestiya. Mathematics , Tome 66 (2002) no. 2, pp. 285-297. http://geodesic.mathdoc.fr/item/IM2_2002_66_2_a1/