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 …

AHMAD ZIREH1 AND MAHMOOD BIDKHAM2 Abstract. For a polynomial p (z) of degree n,
we consider an operator Dα which map a polynomial p (z) into Dαp (z):=(α− z) p (z)+ np (z) …

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) …

SOME INTEGRAL MEAN INEQUALITIES CONCERNING POLAR DERIVATIVE OF A
POLYNOMIAL Let Pn be the class of polynomials P(z) = ∑ cjzj o Page 1 Available online at …

Some inequalities concerning the polar derivative of a polynomial Page 1 © Some inequalities
concerning the polar derivative of a polynomial Abdullah Mir * Ajaz Wani MH Gulzar …

For a rational function r (z)= p (z)/H (z) all zeros of which are in| z|≤ 1, it is known that r′ z≥
1 2 B′ zrz for z= 1,\left| r^ ′ (z)\right| ≥ 1 2\left| B^ ′ (z)\right|\left| r (z)\right|\kern2em …

Let P (z):=∑ j= 0 najzj be a polynomial of degree at most n with real or complex coefficients,
then by a prize winning result of Bernstein max| z|= 1| P′(z)|≤ n max| z|= 1| P (z)|. In this …

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) …

| B (z)|| r (z)| for| z|= 1, where H (z)=∏ nj= 1 (z-cj),| cj|> 1, n is a positive integer, B (z)=
H∗(z)/H (z), and H∗(z)= znH (1/z). In this paper, we improve the above mentioned inequality …

‎ Let $ p (z) $ be a polynomial of degree $ n $ and for a complex number $\alpha $‎,‎ let $ D_
{\alpha} p (z)= np (z)+(\alpha-z) p'(z) $ denote the polar derivative of the polynomial p (z) …