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On closed convex hulls and extreme points of some classes of holomorphic functions

Title
On closed convex hulls and extreme points of some classes of holomorphic functions
Authors
정세원
Issue Date
1991
Department/Major
대학원 수학과
Keywords
closed convex hullsextreme pointsclassesholomorphic functions
Publisher
이화여자대학교 대학원
Degree
Master
Abstract
In the theory of analytic functions the solution to any linear extremal problem can be recuced to its solution over the set of extreme points. In this thesis, we study the integral representation of closed convex hulls of subfamilies of holomorphic functions and find their extreme points, In particular, we derive the extreme points of α-spirallike functions by using the similar method due to G,Schober, We solve the problem given in the book "Univalent functions" by G,Schober[8] and obtain the extreme points of close-to-convex functions of order β ;해석 함수의 이론에서, 임의의 선형 극치 문제의 해는 극점들의 집합으로 축소시켜서 찾을 수 있다. 이논문에서 우리는 해석함수들의 부분족의 닫힌 convex hull의 적분표현을 공부하고 그들의 극점들을 찾는다. 특히 G.Schober에 의한 유사한 방법으로 a-spirallike 함수의 극점을 구한다. 그리고 G.Schober의 "Univalent functions"에 있는 문제를 풀어서 order β의 colse-to-convex 함수들의 극점을 얻는다.
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