Sharpening of Tur´an-type inequality for polynomials
https://doi.org/10.26907/0021-3446-2024-4-39-46
Abstract
For the polynomial P(z) = n \sum j=0 cjzj of degree n having all its zeros in | z| \leq k, k \geq 1, V. Jain in “On the derivative of a polynomial”, Bull. Math. Soc. Sci. Math. Roumanie Tome 59, 339–347 (2016) proved that max | z| =1 | P \prime (z)| \geq n \biggl( | c0| + | cn| kn+1 | c0| (1 + kn+1) + | cn| (kn+1 + k2n) \biggr) max | z| =1 | P(z)| . In this paper we strengthen the above inequality and other related results for the polynomials of degree n \geq 2.
About the Authors
N. A. Rather
University of Kashmir
India
India
Srinagar, 190006
A. Bhat
University of Kashmir
India
India
Srinagar, 190006
M. Shafi
University of Kashmir
India
India
Srinagar, 190006
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Review
For citations:
Rather N.A., Bhat A., Shafi M. Sharpening of Tur´an-type inequality for polynomials. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2024;(4):39-46. (In Russ.) https://doi.org/10.26907/0021-3446-2024-4-39-46
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