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 …

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 …

If P (z) is a polynomial of degree n, and α a complex number, then polar derivative of P (z)
with respect to the point α, denoted by D α P (z), is defined by D α P (z)= n P (z)+(α− z) …

In this paper, we establish some new inequalities in the plane that are inspired by some
classical Bernstein-type inequalities that relate the sup-norm of a polynomial to that of its …

If P (z) is a polynomial of degree n which does not vanish in| z|< 1, then it is recently proved
by Rather Jour. Ineq. Pure and Appl. Math., 9 (2008), Issue 4, Art. 103 that for every γ> 0 and …

INTEGRAL INEQUALITIES FOR THE POLAR DERIVATIVE OF A POLYNOMIAL Page 1 Nonlinear
Functional Analysis and Applications Vol. 23, No. 2 (2018), pp. 381-393 ISSN: 1229-1595(print) …

Let P (z) be a polynomial of degree n, then concerning the estimate for maximum of| P′(z)|
on the unit circle, it was proved by S. Bernstein that∥ P′∥∞≤ n∥ P∥∞. Later, Zygmund …