  Let $ P(z) $ be a polynomial of degree $ n $ having all zeros in $|z|\leq k$
where $k\leq 1,$ then it was proved by Dewan \textit{et al} that for every real
or complex number $\alpha$ with $|\alpha|\geq k$ and each $r\geq 0$
  $$
n(|\alpha|-k)\left\{\int\limits_{0}^{2\pi}\left|P\left(e^{i\theta}\right)\right|^r
d\theta\right\}^{\frac{1}{r}}\leq\left\{\int\limits_{0}^{2\pi}\left|1+ke^{i\theta}\right|^r
d\theta\right\}^{\frac{1}{r}}\underset{|z|=1}{Max}|D_\alpha P(z)|. $$
  \indent In this paper, we shall present a refinement and generalization of
above result and also extend it to the class of polynomials
$P(z)=a_nz^n+\sum_{\nu=\mu}^{n}a_{n-\nu}z^{n-\nu},$ $1\leq\mu\leq n,$ having
all its zeros in $|z|\leq k$ where $k\leq 1$ and thereby obtain certain
generalizations of above and many other known results.
