Inequalities concerning polynomials having zeros in closed interior of a circle
The reviewed paper contains one theorem which is a refinement of some earlier result. Theorem. Let \(p(z)\) be a polynomial of degree \(n\), having all its zeros in \(|z|\leq K\), \(K>1\), then for \(K<R<K^2,\) \[ M\left(p,r\right)\geq r^s\left(\frac{r+K}{1+K}\right)M(p,1)+\frac{r^{n-1}}{K^{n-1}}\left\{\frac{r^{n-s}-1}{Kr^{n-s-1}+1}\right\}m \] where \( M(p,r)=\max_{|z|=r}{|p(z)|}\), \( m=\min_{|z|=K}{|p(z)|} \) and \( s \) is the order of a possible zero of \(p(z)\) at \(z=0\).
scientific article; zbMATH DE number 1625167