A criterion for starlikeness (Q5918024)

An objective of this note is to establish a sufficient condition for starlikeness of maps defined in the unit disk. The condition concerns functions \(f(z)=z+\dots\) continuous in the disk \(\overline\Delta\), analytic in \(\overline\Delta\) except for at most a finite number of points on \(\partial\Delta\) and satisfying on \(\partial\Delta\) certain conditions. Examples are provided that show usefulness of the given conditions.