Sufficient conditions for spiral-likeness
The author gives an extension of the fact that \(\sum^{\infty}_{n=2}n| a_ n| \leq 1\) implies that \(f(z)=z+\sum^{\infty}_{n=2}a_ nz^ n\) is a starlike univalent function of the unit disk \({\mathbb{D}}\), namely if \[ \sum^{\infty}_{n=2}\frac{(n-1)+\sqrt{(n-1)^ 2+4n \cos^ 2 \lambda}}{2 \cos \lambda}| a_ n| \leq 1, \] then f is spirallike of order \(\lambda\), i.e., \[ Re(e^{i\lambda}(zf'(z))/(f(z)))>0\quad (z\in {\mathbb{D}}). \]
scientific article; zbMATH DE number 4127556