- Hacettepe Journal of Mathematics and Statistics
- Vol: 50 Issue: 2
- Starlikeness for certain close-to-star functions
Starlikeness for certain close-to-star functions
Authors : R. Kanaga, V Ravichandran
Pages : 414-432
Doi:10.15672/hujms.702703
View : 13 | Download : 5
Publication Date : 2021-04-11
Article Type : Research
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 $Re(f(z)/g(z))>0$ or $\left|(f(z)/g(z))-1\right|<1$ for some close-to-star function $g$ with $Re(g(z)/(z+z^2/2))>0$ as well as of the class of close-to-star functions $f$ satisfying $Re(f(z)/(z+z^2/2))>0$. 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.Keywords : Univalent functions, convex functions, starlike functions, subordination, radius of starlikeness