Classes of analytic functions subordinate to convex functions and extreme points
Suppose that \(\Delta\) is the unit disk, \(D\) is a convex domain, \(D\neq\mathbb{C}\), \(0\in D\), \(F\) is an analytic and univalent mapping of \(\Delta\) onto \(D\). Let \(s(F)\) denote the set of all analytic functions \(f\) subordinate to \(F\) on \(\Delta\) and let \(Es(F)\) be the set of extreme points. The set \(s(F)\) is known when \(D\) is an infinite wedge, a strip, a half plane or a domain with smooth boundary and piecewise positive curvature but a full description of \(Es(F)\) otherwise is an open problem. Considering the open question the authors of this paper established two new sufficient conditions for \(f\) to be an extreme point of \(s(F)\).
scientific article; zbMATH DE number 1957249