Starlike Functions

An analytic function \(f:\mathbb {D}\rightarrow \mathbb {C}\) is called a starlike function if its image \(f(\mathbb {D})\) is starlike with respect to the origin. The Koebe function is a prominent example of a starlike function. The class of starlike functions shares several properties with the class of univalent functions. This chapter is devoted to the study of starlike functions. An analytic characterization of starlikeness is established and used to derive various properties of functions in this class.