On Visser's inequality concerning coefficient estimates for a polynomial

Abstract

If $P(z)={\sum }_{j=0}^n{a}_j{z}^j$ is a polynomial of degree $n$ having no zero in $|z|<1,$ then it was recently proved that for every $p\in [0,+\infty ]$ 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 $\hat{I}{´}_{0s}$ is the Kronecker delta. In this paper, we consider the class of polynomials having no zero in $|z|<\ddot{I},$ $\ddot{I}\ge 1$ and obtain some generalizations of above inequality.

Polynomials; Visser's inequality; Inequalities in the complex domain