Geodesic
Complex analysis
On the Erdös–Lax inequality concerning polynomials
[Sur l'inégalité d'Erdös–Lax concernant les polynômes]

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Mir, Abdullah1 ; Hussain, Imtiaz1
1 Department of Mathematics, University of Kashmir, Srinagar, 190006, India
Comptes Rendus. Mathématique, Tome 355 (2017) no. 10, pp. 1055-1062.

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Let P(z) be a polynomial of degree n and for any complex number α, let DαP(z):=nP(z)+(α−z)P′(z) denote the polar derivative of P(z) with respect to α. In this paper, we present an integral inequality for the polar derivative of a polynomial. Our theorem includes as special cases several interesting generalisations and refinements of Erdöx–Lax theorem.

Soit P(z) un polynôme de degré n. Pour tout nombre complexe α, notons DαP(z):=nP(z)+(α−z)P′(z) la dérivée polaire de P(z) relative à α. Dans cette Note, nous présentons une inégalité intégrale pour la dérivée polaire. Notre théorème contient comme cas particuliers plusieurs généralisations et raffinements intéressants du théorème d'Erdös et Lax.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.09.017

Mir, Abdullah 1 ; Hussain, Imtiaz 1

1 Department of Mathematics, University of Kashmir, Srinagar, 190006, India 
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Mir, Abdullah; Hussain, Imtiaz. On the Erdös–Lax inequality concerning polynomials. Comptes Rendus. Mathématique, Tome 355 (2017) no. 10, pp. 1055-1062. doi : 10.1016/j.crma.2017.09.017. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2017.09.017/

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