International Journal of Nonlinear Analysis and Applications

Inequalities for the generalized polar derivative of a polynomial

Document Type : Research Paper

Authors

1 Department of Mathematics, University of Kashmir, Srinagar-190006, India

2 Department of Applied Sciences, Institute of Technology, University of Kashmir, Srinagar-190006, India

Abstract

Recently Rather et al. [18] considered the generalized polar derivative and studied the relative position of zeros of the generalized polar derivative with respect to the zeros of the polynomial. In this paper, by taking into account the size of the constant term and the leading coefficient of the polynomial $P(z)$, we obtain some lower bound estimates for the generalized polar derivative of certain polynomials, which refine and generalize various results due to Aziz and Rather, Malik, Tur'{a}n, Dubinin, Govil and others.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 16, Issue 6
June 2025
Pages 153-159
  • Receive Date: 10 September 2021
  • Accept Date: 04 April 2024