Starlikeness for Certain Close-to-Star Functions

Abstract

We find the radius of starlikeness of order $\alpha$, $0\le \alpha <1$, of normalized analytic functions $f$ on the unit disk satisfying either $\mathrm{Re}(f(z)/g(z))>0$ or $\left|(f(z)/g(z))-1\right|<1$ for some close-to-star function $g$ with $\mathrm{Re}(g(z)/(z+z^2/2))>0$ as well as of the class of close-to-star functions $f$ satisfying $\mathrm{Re}(f(z)/(z+z^2/2))>0$. 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.

References in corpus (3)

• Radii of Starlikeness Associated with the Lemniscate of Bernoulli and the Left-Half Plane
• On the radius constants for classes of analytic functions
• Radius of Starlikeness of Certain Analytic Functions

Cited by in corpus (1)

• Starlikeness of certain analytic functions