On the Derivative of a Polynomial

Inequalities for the derivative of a polynomial

“…Let P(z) = ü"=x (z -zf) be a polynomial of degree n having all its zeros in Re z > 1. Is it true that (6) Max|/>'(z)|< S * Max|/>(z)|?…”

Some inequalities for the polar derivative of a polynomial with restricted zeros

“…For a polynomial p(z) of degree at most n which having no zeros in |z| < k, k ≥ 1, inequality (1.2) was generalized by Malik [10] who proved that max |z|=1 |p ′ (z)| ≤ n 1 + k max |z|=1 |p(z)|.…”

On the derivative of a polynomial

“…Another proof of (2) i$ given in [2] where it is deduced by applying the following result (for another proof see [1, Theorem C, p. 503]) to the polynomial znp(l/z). Theorem B.…”