Comptes Rendus
no. 4
Complex analysis
On estimates for the coefficients of a polynomial
Presented by: the Editorial Board
Suhail Gulzar 1
1 Islamic University of Science and Technology, Kashmir, Awantipora 192122, India
Comptes Rendus. Mathématique, Volume 354 (2016) no. 4, pp. 357-363

If P(z)=∑j=0najzj is a polynomial of degree n, then it was proved by Rahman and Schmeisser [4] that for every p∈[0,+∞],

|an|+|a0|≤2‖P‖p‖1+z‖p.
In this paper, various estimates for the coefficients of a polynomial P are obtained which among other things include the above inequality as a special case.

Si P(z)=∑j=0najzj est un polynôme de degré n, Rahman et Schmeisser [4] ont montré que, pour tout p∈[0,+∞], on a

|an|+|a0|≤2‖P‖p‖1+z‖p.
Nous obtenons ici diverses majorations pour les coefficients d'un polynôme qui, entre autres, incluent l'inégalité ci-dessus comme cas particulier.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.01.018

Suhail Gulzar  1

1 Islamic University of Science and Technology, Kashmir, Awantipora 192122, India 
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Suhail Gulzar. On estimates for the coefficients of a polynomial. Comptes Rendus. Mathématique, Volume 354 (2016) no. 4, pp. 357-363. doi: 10.1016/j.crma.2016.01.018

[1] V.V. Arestov On integral inequalities for trigonometric polynomials and their derivatives, Izv. Akad. Nauk SSSR, Ser. Mat., Volume 45 (1981), pp. 3-22 (in Russian); English translation: Math. USSR, Izv., 18, 1982, pp. 1-17

[2] R.B. Gardner; N.K. Govil An Lp inequality for a polynomial and its derivative, J. Math. Anal. Appl., Volume 193 (1995), pp. 490-496

[3] Q.I. Rahman; G. Schmeisser Analytic Theory of Polynomials, Oxford University Press, New York, 2002

[4] Q.I. Rahman; G. Schmeisser Lp inequalities for polynomial, J. Approx. Theory, Volume 53 (1988), pp. 26-32

[5] C. Visser A simple proof of certain inequalities concerning polynomials, Proc. K. Ned. Akad. Wet., Volume 47 (1945), pp. 276-281

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