<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>According to Gauss-Lucas theorem, every convex set containing all the zeros of a polynomial also contains all its critical points. This result is of central importance in the geometry of critical points in the analytic theory of polynomials. In this paper, an extension of Gauss-Lucas theorem is obtained and as an application some generalizations of Bernstein-type polynomial inequalities are also established.</p>
</abstract>

According to Gauss-Lucas theorem, every convex set containing all the zeros of a polynomial also contains all its critical points. This result is of central importance in the geometry of critical points in the analytic theory of polynomials. In this paper, an extension of Gauss-Lucas theorem is obtained and as an application some generalizations of Bernstein-type polynomial inequalities are also established.

Gauss Lucas theorem and Bernstein-type inequalities for polynomials

Acta Universitatis Sapientiae, Mathematica

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

{"article-title":"Gauss Lucas theorem and Bernstein-type inequalities for polynomials"}

According to Gauss-Lucas theorem, every convex set containing all the zeros of a polynomial also contains all its critical points. This result is of central...

Gauss Lucas theorem and Bernstein-type inequalities for polynomials

Published Online: Jan 19, 2023

Page range: 211 - 219

Received: Sep 09, 2021

DOI: https://doi.org/10.2478/ausm-2022-0013

Keywords
Gauss Lucas theorem, inequalities in the complex domain, polynomials

© 2022 Liyaqat Ali et al., published by Sciendo

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

Gauss Lucas theorem and Bernstein-type inequalities for polynomials

Published Online: Jan 19, 2023

Page range: 211 - 219

Received: Sep 09, 2021

DOI: https://doi.org/10.2478/ausm-2022-0013

KeywordsGauss Lucas theorem, inequalities in the complex domain, polynomials

© 2022 Liyaqat Ali et al., published by Sciendo

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

Keywords
Gauss Lucas theorem, inequalities in the complex domain, polynomials