Geodesic
On polynomials and rational functions normalized on the circular arcs
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 28, Tome 418 (2013), pp. 105-120

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Applications of the geometric theory of functions to some inequalities for algebraic polynomials and rational functions normalized on the circular arcs are considered. In particular, coefficients estimates, covering and distortion theorems are obtained. These theorems supplement recent results of the author and V. N. Dubinin. 
@article{ZNSL_2013_418_a6,
     author = {S. I. Kalmykov},
     title = {On polynomials and rational functions normalized on the circular arcs},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {105--120},
     publisher = {mathdoc},
     volume = {418},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_418_a6/}
}
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S. I. Kalmykov. On polynomials and rational functions normalized on the circular arcs. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 28, Tome 418 (2013), pp. 105-120. http://geodesic.mathdoc.fr/item/ZNSL_2013_418_a6/