Integral mean estimates for the polar derivative of a polynomial

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