<abstract xmlns="http://www.w3.org/1999/xhtml">
Let <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amsil-2023-0016_eq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>P</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><msubsup><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>0</mn></mrow><mi>n</mi></msubsup><mrow><msub><mrow><mi>a</mi></mrow><mi>j</mi></msub><msup><mrow><mi>z</mi></mrow><mi>j</mi></msup></mrow></mrow></math>
<tex-math>P\left( z \right) = \sum\nolimits_{j = 0}^n {{a_j}{z^j}}</tex-math>
</alternatives>
</inline-formula> be a polynomial of degree <italic>n </italic>such that <italic>a</italic><italic>n </italic> ≥ <italic>a</italic><italic>n−</italic>1 ≥ . . . ≥ <italic>a</italic>1 ≥ <italic>a</italic>0 ≥ 0. Then according to Eneström-Kakeya theorem all the zeros of <italic>P </italic>(<italic>z</italic>) lie in <italic>|z| ≤ </italic>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].
</abstract>

Let 


P(z)=∑j=0najzj
P\left( z \right) = \sum\nolimits_{j = 0}^n {{a_j}{z^j}}

 be a polynomial of degree n such that an  ≥ an−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].

On the Zeros of Polynomials with Restricted Coefficients

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"On the Zeros of Polynomials with Restricted Coefficients"}

Let 


P(z)=∑j=0najzj
P\left( z \right) = \sum\nolimits_{j = 0}^n {{a_j}{z^j}}

 be a polynomial of degree n such that an  ≥ an−1 ≥ . . . ≥ a1 ≥ a0 ≥ 0. Then...

On the Zeros of Polynomials with Restricted Coefficients

Data publikacji: 13 wrz 2023

Zakres stron: 306 - 314

Otrzymano: 21 sty 2023

Przyjęty: 17 sie 2023

DOI: https://doi.org/10.2478/amsil-2023-0016

Słowa kluczowe
polynomial, zeros, restricted coefficients

© 2023 B. A. Zargar et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

On the Zeros of Polynomials with Restricted Coefficients

Data publikacji: 13 wrz 2023

Zakres stron: 306 - 314

Otrzymano: 21 sty 2023

Przyjęty: 17 sie 2023

DOI: https://doi.org/10.2478/amsil-2023-0016

Słowa kluczowepolynomial, zeros, restricted coefficients

© 2023 B. A. Zargar et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Słowa kluczowe
polynomial, zeros, restricted coefficients