Kortram, R. A. The extreme points of a class of functions with positive real part. (English) Zbl 0914.30013 Bull. Belg. Math. Soc. - Simon Stevin 4, No. 4, 449-459 (1997). Let \(H(\Delta)\) denote the set of analytic functions on the unit disk \(\Delta\), and let \(P\subset H(\Delta)\) consist of functions \(f\) with positive real part and normalized by \(f(0)= 1\). The extreme points of \(P\) are known. The author provides a different proof to determine the extreme points, which uses elementary functional analysis.The set \(F\subset H(\Delta)\) consist of functions \(f\) with \(f(0)= 0\) and \(-\pi/2< \text{Im }f(z)< \pi/2\). The author determines the extreme points of \(F\) with a simpler proof than what is in the literature.For \(0<\alpha< 1\), the set \(P_\alpha\subset P\) consists of functions that satisfy the inequality \(|\text{arg }f|< \alpha\pi/2\). The author finds the extreme points of \(P_\alpha\). Reviewer: Renate McLaughlin (Flint) Cited in 1 Document MSC: 30C75 Extremal problems for conformal and quasiconformal mappings, other methods 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) Keywords:extreme points; integral representative; elementary functional analysis PDFBibTeX XMLCite \textit{R. A. Kortram}, Bull. Belg. Math. Soc. - Simon Stevin 4, No. 4, 449--459 (1997; Zbl 0914.30013) Full Text: EuDML