On the Zeros of Polynomials with Restricted Coefficients

Zargar, B. A.; Gulzar, M. H.; Ali, M.

doi:10.2478/amsil-2023-0016

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On the Zeros of Polynomials with Restricted Coefficients

Annales Mathematicae Silesianae

Volume 37 (2023): Issue 2 (September 2023)

By: B. A. Zargar, M. H. Gulzar and M. Ali

Open Access

|Sep 2023

Abstract

Let $P (z) = \sum_{j = 0}^{n} a_{j} z^{j}$ P\left( z \right) = \sum\nolimits_{j = 0}^n {{a_j}{z^j}} be a polynomial of degree n such that a_n ≥ a_n−₁ ≥ . . . ≥ a₁≥ a₀≥ 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].

References

A. Aziz and B.A. Zargar, Some extensions of Eneström–Kakeya theorem, Glas. Mat. Ser. III 31(51) (1996), no. 2, 239–244.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
K.K. Dewan and M. Bidkham, On the Eneström–Kakeya theorem, J. Math. Anal. Appl. 180 (1993), no. 1, 29–36.
Search in Google Scholar Back to article
N.K. Govil and Q.I. Rahman, On the Eneström–Kakeya theorem, Tohoku Math. J. (2) 20 (1968), 126–136.
Search in Google Scholar Back to article
M. Marden, Geometry of Polynomials, Math. Surveys, No. 3, American Mathematical Society, Providence, RI, 1966.
Search in Google Scholar Back to article
G.V. Milovanović and A. Mir, Zeros of one class of quaternionic polynomials, Filomat 36 (2022), no. 19, 6655–6667.
Search in Google Scholar Back to article
E.R. Nwaeze, Some generalizations of the Eneström–Kakeya theorem, Acta Comment. Univ. Tartu. Math. 20 (2016), no. 1, 15–21.
Search in Google Scholar Back to article

DOI: https://doi.org/10.2478/amsil-2023-0016 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 306 - 314

Submitted on: Jan 21, 2023

Accepted on: Aug 17, 2023

Published on: Sep 13, 2023

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

polynomial,

zeros,

restricted coefficients

Related subjects:

Mathematics,

General mathematics

© 2023 B. A. Zargar, M. H. Gulzar, M. Ali, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

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