Convex hulls and extreme points of some families of multivalent functions
An objective of this paper is to determine the convex hulls and their extreme points for some classes of p-valent starlike functions in the unit disk that are normalized by the conditions \[ f(z_ 0)=z^ p_ 0,f(z)=a_ 0z^ p+\sum^{\infty}_{k=2}a_ kz^{k+p}, \] \(z_ 0\) being a given complex number, \(z_ 0\neq 0\). These results reduce in the case \(p=1\) to earlier ones due to \textit{M. Fait} and the reviewer [Ann. Univ. Marie Curie-Skłodowska, Sect A 30, 35-41 (1976; Zbl 0413.30010)] or \textit{H. Silverman} [Proc. Am. Math. Soc. 51, 109-116 (1975; Zbl 0311.30007)].
scientific article; zbMATH DE number 4069264