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 …

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) …

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) …

Recently Rather et al.[18] considered the generalized polar derivative and studied the
relative position of zeros of the generalized polar derivative with respect to the zeros of the …

P. Turán was the first to derive lower estimations on the uniform norm of the derivatives of
polynomials p of uniform norm 1 on the disk D:={z∈ C:| z|≤ 1} and the interval I:=[− 1, 1] …

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 …

For the polar derivative D α P ( z ) = n P ( z ) + ( α - z ) P ′ ( z ) \documentclass[12pt]{minimal}
\usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} …

208 NA Rather Both these estimates are sharp and equality holds for P (z)= az n, a= 0.
Inequality (1) is well known result of Bernstein (see [10] or [13]) whereas inequality (2) is due …

On Arestov’s inequalities concerning the Shur–Szegő composition of polynomials | Periodica
Mathematica Hungarica Skip to main content SpringerLink Account Menu Find a journal …

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) …