Inequalities for polynomials and their derivatives are very important in many areas of
mathematics, as well as in other computational and applied sciences; in particular they play …

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) …

Lγ Inequalities for the Polar Derivative of Polynomials Abstract Page 1 Malaysian Journal of
Mathematical Sciences 17(3): 333–347 (2023) https://doi.org/10.47836/mjms.17.3.06 …

and (1.2) P p≤ nPp. Inequality (1.1) is a well-known result of S. Bernstein (see [12] or [15]),
whereas inequality (1.2) is due to Zygmund [16]. Arestov [1] proved that the inequality (1.2) …

Let p (z) be a polynomial of degree n and α be any real or complex number, the polar
derivative of p (z), denoted by D α p (z), is defined as D α p (z)= np (z)+(α-z) p′(z). Let p (z) …

In this paper, we sharpen some of the known results of polar derivative of a polynomial by
establishing the L< sup> q-version of a known inequality on the polar derivative of a …

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) …

This paper contains the finding of some upper bound estimates for the maximal modulus of a
lacunary polynomial of degree n on a circle of radius 0< r≤ R≤ k under the assumption that …

We establish some-inequalities for the polar derivative of a polynomial. Our results
generalize some known Bernstein-type polynomial inequalities and include as special …

Получены Lγ-неравенства для полярной производной полинома. Результаты
обобщают известные полиномиальные неравенства типа Бернштейна, а также …