On the Erdös–Lax inequality concerning polynomials

Abdullah Mir; Imtiaz Hussain

doi:10.1016/j.crma.2017.09.017

Complex analysis

On the Erdös–Lax inequality concerning polynomials

Presented by: the Editorial Board

Abdullah Mir ¹; Imtiaz Hussain ¹

¹ Department of Mathematics, University of Kashmir, Srinagar, 190006, India

Comptes Rendus. Mathématique, Volume 355 (2017) no. 10, pp. 1055-1062.

Abstract (Original language)
Résumé

Let $P (z)$ be a polynomial of degree n and for any complex number α, let $D_{α} P (z) : = n P (z) + (α - z) P^{'} (z)$ 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 $D_{α} P (z) : = n P (z) + (α - z) P^{'} (z)$ 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.

Received: 2016-06-10
Accepted: 2017-09-29
Published online: 2017-10-01

DOI: 10.1016/j.crma.2017.09.017

Author's affiliations:

Abdullah Mir ¹; Imtiaz Hussain ¹

¹ Department of Mathematics, University of Kashmir, Srinagar, 190006, India

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     title = {On the {Erd\"os{\textendash}Lax} inequality concerning polynomials},
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Abdullah Mir; Imtiaz Hussain. On the Erdös–Lax inequality concerning polynomials. Comptes Rendus. Mathématique, Volume 355 (2017) no. 10, pp. 1055-1062. doi : 10.1016/j.crma.2017.09.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.09.017/

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