Geodesic
On polynomials normalized on an interval
Dalʹnevostočnyj matematičeskij žurnal, Tome 18 (2018) no. 2, pp. 216-266

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In this short communication new covering theorems, two-point distortion theorems and coefficient estimates for polynomials with a curved majorant on an interval are presented. Extremal polynomials in these therems are Chebyshev polynomials of the the second, third and forth kinds. Proofs are based on a new version of the Schwarz lemma and a univalent condition for holomorphic functions suggested by Dubinin. 
@article{DVMG_2018_18_2_a9,
     author = {S. I. Kalmykov},
     title = {On polynomials normalized on an interval},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {216--266},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2018_18_2_a9/}
}
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S. I. Kalmykov. On polynomials normalized on an interval. Dalʹnevostočnyj matematičeskij žurnal, Tome 18 (2018) no. 2, pp. 216-266. http://geodesic.mathdoc.fr/item/DVMG_2018_18_2_a9/