Starlikeness for Certain ClosetoStar Functions
Abstract
We find the radius of starlikeness of order $\alpha$, $0\leq \alpha<1$, of normalized analytic functions $f$ on the unit disk satisfying either $\operatorname{Re}(f(z)/g(z))>0$ or $\left (f(z)/g(z))1\right<1$ for some closetostar function $g$ with $\operatorname{Re}(g(z)/(z+z^2/2))>0$ as well as of the class of closetostar functions $f$ satisfying $\operatorname{Re}(f(z)/(z+z^2/2))>0$. Several other radii such as radius of univalence and parabolic starlikeness are shown to be the same as the radius of starlikeness of appropriate order.
 Publication:

arXiv eprints
 Pub Date:
 March 2020
 DOI:
 10.48550/arXiv.2003.05628
 arXiv:
 arXiv:2003.05628
 Bibcode:
 2020arXiv200305628K
 Keywords:

 Mathematics  Complex Variables;
 30C80;
 30C45