Geodesic
Distortion theorem for complex polynomials
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1410-1415

Voir la notice de l'article provenant de la source Math-Net.Ru

For any complex polynomial $P$ of degree $n\ge 2$ and any complex number $z$, we consider a sharp inequality involving of the absolute values of $P(z),\; P'(z)$, leading coefficient of $P$ and an upper bound of the moduli of the critical values of $P$. All cases of an equality in this inequality are established.
Keywords: distortion theorems, complex polynomials, inequalities, critical values. 
@article{SEMR_2018_15_a139,
     author = {V. N. Dubinin},
     title = {Distortion theorem for complex polynomials},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1410--1415},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a139/}
}
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V. N. Dubinin. Distortion theorem for complex polynomials. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1410-1415. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a139/