On an upper bound for the polar derivative of a polynomial
Abstract
Liman, Mohopatra and Shah proved that if p(z) is a polynomial of degree n having no zeros in |z| < 1, then for all α,β ∈ C with |α| ≥ 1, |β| ≤ 1 and |z| = 1,
where Dαp(z) = np(z) + (α − z)p’(z) is the polar derivative of p(z) with respect to the point α. We extend and generalize this inequality for the polynomial p(z) which does not vanish in |z| < k, k ≤ 1. Our result also generalizes other known inequalities as well.
Copyright © 2021 Kshetrimayum Krishnadas, Barchand Chanam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
K. Krishnadas, B. Chanam, On an upper bound for the polar derivative of a polynomial, J. Math. Comput. Sci. 11 (2021), 6491–6506. https://doi.org/10.28919/jmcs/6162
BibTeX
@article{Krishnadas2021,
author = {Krishnadas, Kshetrimayum and Chanam, Barchand},
title = {On an upper bound for the polar derivative of a polynomial},
journal = {J. Math. Comput. Sci.},
volume = {11},
year = {2021},
pages = {6491--6506},
doi = {10.28919/jmcs/6162}
}