Growth of the sth derivative of a polynomial with restricted zeros

Document Type : Research Paper

Authors

Department of Mathematics, National Institute of Technology Manipur, Manipur-795004, India

10.22075/ijnaa.2023.27169.3521

Abstract

In this paper, we establish some upper bound estimates for the maximum modulus of the higher order derivative of a polynomial with restricted zeros on a circle of $|z|=R$, $R\geq 1$, in terms of the maximum modulus of the same polynomial on the unit circle $|z|=1$. These results generalize and sharpen some known results in this direction.

Keywords


Articles in Press, Corrected Proof
Available Online from 14 August 2023
  • Receive Date: 14 May 2022
  • Revise Date: 10 August 2023
  • Accept Date: 12 August 2023