no. 10
Complex analysis
On the Erdös–Lax inequality concerning polynomials
[Sur l'inégalité d'Erdös–Lax concernant les polynômes]

Présenté par : the Editorial Board

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.

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.

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.

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://www.numdam.org/articles/10.1016/j.crma.2017.09.017/

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