Local discriminate theorem for extreme points of families of analytic functions. (Chinese. English summary) Zbl 0688.30017

Chang, Nengming

Acta Sci. Nat. Univ. Sunyatseni 28, No. 2, 10-14 (1989).

Using the local property of the boundary curve of a domain D, we present several theorems concerning the sufficient conditions of extreme points of families of analytic functions which map the unit disk to D. In particular, we have characterized the extreme points of families of analytic functions that are subordinating to some special classes of analytic functions.

Reviewer: C.-C.Yang

MSC:

30C75	Extremal problems for conformal and quasiconformal mappings, other methods
30C80	Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination

Keywords:

differentiable boundary curve; curvature; extreme points; subordinating