Integral inequality for the polar derivative of a lacunary-type complex polynomial

Document Type : Research Paper

Author

School of Mathematics, Renmin University of China, Beijing, 100872, China

10.22075/ijnaa.2021.23300.2516

Abstract

Let P(z) be a polynomial of degree n and for any complex number, let
$$D_{\alpha}P(z) = nP(z) + (\alpha-z)P'(z)$$
denote the polar derivative of P(z) with respect to a complex number $\alpha$. In this paper, we prove some integral-norm inequalities for the polar derivative of a lacunary-type complex polynomial, which have no zeros in $|z|< k; k \geq 1$, and thereby obtain generalizations of many known results.

Keywords


Articles in Press, Accepted Manuscript
Available Online from 08 September 2023
  • Receive Date: 30 April 2021
  • Revise Date: 07 July 2021
  • Accept Date: 31 July 2021