On the zeros of polynomials with restricted coefficients



Abstract

Let P(z) = Σj=0najzj be a polynomial of degree n such that anan-1 ≥ ... ≥ a1a0 ≥ 0. Then according to Eneström-Kakeya theorem all the zeros of P(z) lie in |z| ≤ 1. This result has been generalized in various ways (see [1, 3, 4, 6, 7]). In this paper we shall prove some generalizations of the results due to Aziz and Zargar [1, 2] and Nwaeze [7].

 

Keywords

polynomial; zeros; restricted coefficients

A. Aziz and B.A. Zargar, Some extensions of Eneström–Kakeya theorem, Glas. Mat. Ser. III 31(51) (1996), no. 2, 239–244.

A. Aziz and B.A. Zargar, Bounds for the zeros of a polynomial with restricted coefficients, Appl. Math. (Irvine) 3 (2012), no. 1, 30–33.

K.K. Dewan and M. Bidkham, On the Eneström–Kakeya theorem, J. Math. Anal. Appl. 180 (1993), no. 1, 29–36.

N.K. Govil and Q.I. Rahman, On the Eneström–Kakeya theorem, Tohoku Math. J. (2) 20 (1968), 126–136.

M. Marden, Geometry of Polynomials, Math. Surveys, No. 3, American Mathematical Society, Providence, RI, 1966.

G.V. Milovanović and A. Mir, Zeros of one class of quaternionic polynomials, Filomat 36 (2022), no. 19, 6655–6667.

E.R. Nwaeze, Some generalizations of the Eneström–Kakeya theorem, Acta Comment. Univ. Tartu. Math. 20 (2016), no. 1, 15–21.

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Published : 2023-09-13


ZargarB. A., GulzarM. H., & AliM. (2023). On the zeros of polynomials with restricted coefficients. Annales Mathematicae Silesianae, 37(2), 306-314. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/15112

B. A. Zargar 
Department of Mathematics, University of Kashmir  India
M. H. Gulzar 
Department of Mathematics, University of Kashmir  India
M. Ali  alimansoor.ma786@gmail.com
Department of Mathematics, University of Kashmir  India



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