For a polynomial
P(
z) of degree n having no zeros in |
z| < 1, it was recently proved in 9] that
$$\left| {{z^s}{P^{\left( s \right)}}\left( z \right) + \beta \frac{{n\left( {n - 1} \right)...\left( {n - s + 1} \right)}}{{{2^s}}}P\left( z \right)} \right| \leqslant \frac{{n\left( {n - 1} \right)...\left( {n - s + 1} \right)}}{2}\left( {\left| {1 + \frac{\beta }{{{2^s}}}} \right| + \left| {\frac{\beta }{{{2^s}}}} \right|} \right)\mathop {\max }\limits_{\left| z \right| = 1} \left| {P\left( z \right)} \right|$$
for every β ∈ C with |β| ≤ 1, 1 ≤
s ≤
n and |
z| = 1. In this paper, we obtain the
L p mean extension of the above and other related results for the sth derivative of polynomials.