arXiv subjects

M. Bidkham

Publications and source records attributed to M. Bidkham.

2 recordsLinked to original sources

arXiv2009

Inequalities for the Polar Derivative of a Polynomial

In this paper we obtain new results concerning maximum modulus of the polar derivative of a polynomial with restricted zeros. Our results generalize and refine upon the results of Aziz and Shah [An integral mean estimate for polynomial, Indian J. Pure Appl. Math. 28 (1997) 1413--1419] and Gardner, Govil and Weems [Some result concerning rate of growth of polynomials, East J. Apporox. 10(2004) 301--312].

math.CV↗

arXiv2009

An operator product inequalities for polynomials

Let $P(z)$ be a polynomial of degree $n\geq 1$. In this paper we define an operator $B$, as following, $$B[P(z)]:=λ_0 P(z)+λ_1 (\frac{nz}{2}) \frac{P'(z)}{1!}+λ_2 (\frac{nz}{2})^2 \frac{P''(z)}{2!},$$ where $λ_0,λ_1$ and $λ_2$ are such that all the zeros of $$u(z)=λ_0 +c(n,1)λ_1 z+c(n,2) λ_2 z^2$$ lie in half plane $$|z|\leq |z-\frac{n}{2}|$$ and obtain a new generalization of some well-known results.

math.CV↗