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 …

Let P (z) be a polynomial of degree n. We consider an operator Dα that maps P (z) into DαP
(z):= nP (z)+(α− z) P0 (z) and establish some results concerning the estimates of 1DαP (z) 1 …

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) …

Let P (z) be a polynomial of degree n and for any complex number α, let Dα P (z)= nP
(z)+(αa z) P (z) denote the polar derivative of the polynomial P (z) with respect to α. In this …

We prove some results for algebraic polynomials in the complex plane that relate the L-norm
of the polar derivative of a complex polynomial and the polynomial under some conditions …

Let $ P (z) $ be a polynomial of degree $ n $ and for any complex number $\alpha $, let $$
D_ {\alpha} P (z)= nP (z)+(\alpha-z) P^{\prime}(z) $$ denote the polar derivative of $ P (z) …

Let P (z) be a polynomial of degree n. We consider an operator Dα that maps P (z) into DαP
(z):= nP (z)+(α-z) P (z) and establish some results concerning the estimates of| DαP (z)| on …

Some integral inequalities for a polynomial with zeros outside the unit disk Page 1 Acta Univ.
Sapientiae, Mathematica, 13, 2 (2021) 396–412 DOI: 10.2478/ausm-2021-0024 Some …

In this paper, we establish some integral-norm estimates for lacunary-type polynomials in
the complex plane that are inspired by some classical Bernstein-type inequalities that relate …

Let p (z) be a polynomial of degree n and for α∈ C, let D α p (z):= np (z)+(α− z) p′(z)
denote the polar derivative of the polynomial p (z) with respect to α. In this paper, we obtain …