On Visser's inequality concerning coefficient estimates for a polynomial

S. Gulzar ; N. A. Rather ; M. Sh. Wani

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2022), pp. 13-20

Résumé

If $P(z)=\sum\limits_{j=0}^{n}a_jz^j$ 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 $s=0,1,\ldots,n-1,$ \begin{align*} \left\|a_nz+\frac{a_s}{\binom{n}{s}}\right\|_{p}\leq \frac{\left\|z+\delta_{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 $|z|\rho,$ $\rho\geq 1$ and obtain some generalizations of above inequality.

Détail

Mots-clés : polynomial
Keywords: Visser's inequality, inequality in the complex domain.