Starlikeness for Certain Close-to-Star Functions

R. Kanaga; V. Ravichandran

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arXiv · 2003.05628

Starlikeness for Certain Close-to-Star Functions

R. Kanaga·V. Ravichandran

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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 close-to-star function $g$ with $\operatorname{Re}(g(z)/(z+z^2/2))>0$ as well as of the class of close-to-star 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.

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R. Kanaga, V. Ravichandran. 2020-03-12. Starlikeness for Certain Close-to-Star Functions. https://arxiv.org/abs/2003.05628

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