Generalizations of Bernstein-type inequalities for polynomials involving the polar derivative

I. Hussain

National Institute of Technology Srinagar

Abstract: We establish some $L^\gamma$-inequalities for the polar derivative of a polynomial. Our results generalize some known Bernstein-type polynomial inequalities and include as special cases several interesting generalizations of some Zygmund-type inequalities for polynomials as well.

Keywords: polar derivative, $L^\gamma$-inequality, zeros.

UDC: 517.54

MSC: 35R30

Received: 27.05.2021
Revised: 15.01.2022
Accepted: 10.02.2022

DOI: 10.33048/smzh.2022.63.316

 English version: Siberian Mathematical Journal, 2022, 63:3, 575–582

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