Let P (z) be a polynomial of degree n and for any complex number α, let D α P (z):= n P
(z)+(α− z) P′(z) denote the polar derivative of P (z) with respect to α. In this paper, we …

The goal of this paper is to extend to the polar derivatives some previous inequalities
between the L^ γ L γ-norms of the derivative and of the polynomial itself, in case when the …

Let p (z) be a polynomial of degree n and for any real or complex number α, let Dαp (z)= np
(z)+(α− z) p′(z) denote the polar derivative of the polynomial p (z) with respect to α. In this …

We prove that if P (z) is a polynomial of degree n with zeros zm, that satisfy| z_m| ≧ K_m ≧
1| zm|≥ K m≥ 1, 1 ≦ m ≦ n 1≤ m≤ n, then for any p> 0, and for every complex number α …

In this paper, we establish some Bernstein-type integral inequalities for a certain class of
polynomials involving the polar derivative. Our results generalize some known polynomial …

1 Introduction and statement of results Page 1 Bull. Math. Soc. Sci. Math. Roumanie Tome 62
(110) No. 2, 2019, 163–172 On Zygmund-type inequalities involving polar derivative of a …

By using the boundary Schwarz lemma, it was shown by Dubinin (J Math Sci 143: 3069–
3076, 2007) that if P (z) is a polynomial of degree n having all its zeros in| z| ≤ 1,| z|≤ 1 …

POLYNOMIALS WITH POLAR DERIVATIVES Abdullah Mir, Ajaz Wani 1. Introduction Let Pn be
the class of polynomials of degree n and we Page 1 Functiones et Approximatio 55.2 (2016) …

Some Applications Of The Boundary Schwarz Lemma For Polynomials With Restricted Zeros∗
Page 1 Applied Mathematics E-Notes, 20(2020), 422-431 c ISSN 1607-2510 Available free at …

SOME EXTENSIONS OF A THEOREM OF PAUL TURÁN CONCERNING POLYNOMIALS 1.
Introduction In scientific disciplines like physics, engin Page 1 Kragujevac Journal of …