On Visser's inequality concerning coefficient estimates for a polynomial

If $P(z)={\sum }_{j=0}^n{a}_j{z}^j$ is a polynomial of degree $n$ having no zero in $\mathrm{\mid }z\mathrm{\mid }<1,$ then it was recently proved that for every $p\in [0,+\mathrm{\infty }]$ and $s=0,1,\dots ,n-1,$ \begin{align*} \left|a_nz+\frac{a_s}{\binom{n}{s}}\right|{p}\leq \frac{\left|z+δ{0s}\right|_p}{\left|1+z\right|p}\left|P\right|{p}, \end{align*} where ${\delta }_{0s}$ is the Kronecker delta. In this paper, we consider the class of polynomials having no zero in $\mathrm{\mid }z\mathrm{\mid }<\rho ,$ $\rho \ge 1$ and obtain some generalizations of above inequality.