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Geometric Properties for Some Classes of Holomorphic Functions

Title
Geometric Properties for Some Classes of Holomorphic Functions
Authors
심희정
Issue Date
1997
Department/Major
대학원 수학과
Keywords
Geometric PropertiesHolomorphic FunctionsSome Classes
Publisher
이화여자대학교 대학원
Degree
Master
Abstract
본 논문에서는 H.Silverman이 발표한 함수족 C_(p)[α,β)을 공부하고, 그 함수족의 조건 중 볼록함수 φ(z) 대신에 극치함수 □를 대입하여 새로운 함수족 C[φ_(0),α], CS[φ_(0),α]를 구성하고, 이들의 몇가지 기하학적 성질을 증명한다. 또한 starlike 함수족의 부분함수족 R[α]를 소개하고, 이 함수족의 몇가지 성질을 유도한다.;H. Silverman constructed a class C_(p)[α,β] of close-to-convex functions. In this thesis, we study a subclass C[φ_(0),α] of C_(p)[α,β], where φ_(0)(z)=z/1-e^(it)z is the extremal convex function and a subclass CS[φ_(0),α] of close-to-star functions in the unit disk. Moreover, we study the class R[α] with the condition Re[f′(z)+ zf″(z)] > α. In this thesis, we obtain several geometric properties for the classes C[φ_(0),α], CS[φ_(0),α] and R[α] including the distortion theorem, covering theorem and the radius of convexity problem, etc.
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