Generalization of Zygmund type inequalities for the sth derivative of polynomials
Abstract
If p(z) is a polynomial of degree n and p(z) ≠ 0 in |z| < 1, it was proved by Hans and Lal [Anal. Math. 40, 105-115(2014)] that for any β ∈ C with |β| ≤ 1,1 ≤ s ≤ n,
In this paper, we prove an inequality which gives an improved and generalized extension of the above inequality into Lγ norm.
Copyright © 2021 Reingachan Ngamchui, Birkramjit Singh, 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
R. Ngamchui, B. Singh, B. Chanam, Generalization of Zygmund type inequalities for the sth derivative of polynomials, J. Math. Comput. Sci. 11 (2021), 5140–5155. https://doi.org/10.28919/jmcs/5934
BibTeX
@article{Ngamchui2021,
author = {Ngamchui, Reingachan and Singh, Birkramjit and Chanam, Barchand},
title = {Generalization of Zygmund type inequalities for the sth derivative of polynomials},
journal = {J. Math. Comput. Sci.},
volume = {11},
year = {2021},
pages = {5140--5155},
doi = {10.28919/jmcs/5934}
}