Growth of polynomials not vanishing in a disk
Abstract
This paper deals with the problem of finding some upper bound estimates for the maximal modulus of a lacunary polynomial on a disk of radius R, R≥1 under the assumption that the polynomial does not vanish in another disk with radius k, k≥1. Our results sharpen as well as generalize a result recently proved by Hussain [Indian J. Pure Appl. Math., (https://doi.org/10.1007/s13226-021-00169-7)]. Further, these results generalize as well as sharpen some known results in this direction.
Copyright © 2021 Khangembam Babina Devi, Maisnam Triveni Devi, N. Reingachan, 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. B. Devi, M. T. Devi, N. Reingachan, B. Chanam, Growth of polynomials not vanishing in a disk, J. Math. Comput. Sci. 12 (2022), 17. https://doi.org/10.28919/jmcs/6864
BibTeX
@article{Devi2022,
author = {Devi, Khangembam Babina and Devi, Maisnam Triveni and Reingachan, N. and Chanam, Barchand},
title = {Growth of polynomials not vanishing in a disk},
journal = {J. Math. Comput. Sci.},
volume = {12},
year = {2022},
pages = {17},
doi = {10.28919/jmcs/6864}
}