Soit un polynôme de degré n. Pour tout nombre complexe α, notons la dérivée polaire de 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 be a polynomial of degree n and for any complex number α, let denote the polar derivative of 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.
Accepté le :
Publié le :
Abdullah Mir 1 ; Imtiaz Hussain 1
@article{CRMATH_2017__355_10_1055_0, author = {Abdullah Mir and Imtiaz Hussain}, title = {On the {Erd\"os{\textendash}Lax} inequality concerning polynomials}, journal = {Comptes Rendus. Math\'ematique}, pages = {1055--1062}, publisher = {Elsevier}, volume = {355}, number = {10}, year = {2017}, doi = {10.1016/j.crma.2017.09.017}, language = {en}, }
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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