Starlikeness of certain analytic functions

Abstract

Let $f$ and $g$ be analytic functions on the open unit disk of the complex plane with $f/g$ belonging to the class $\mathcal{P}$ of functions with positive real part consisting of functions $p$ with $p(0)=1$ and $\mathrm{Re}p(z)>0$ or to its subclass consisting of functions $p$ with $|p(z)-1|<1$. We obtain the sharp radius constants for the function $f$ to be starlike of order $\alpha$, parabolic starlike, etc. when $g/k\in \mathcal{P}$ where $k$ denotes the Koebe function defined by $k(z)=z/(1-z{)}^2$.

References in corpus (1)

• Radius of Starlikeness for Classes of Analytic Functions

Cited by in corpus (1)

• Inclusion relations and radius problems for a subclass of starlike functions