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Extreme points of class of spiral functions and its application

Title
Extreme points of class of spiral functions and its application
Authors
정계선
Issue Date
1990
Department/Major
대학원 수학과
Publisher
이화여자대학교 대학원
Degree
Doctor
Abstract
F_α,ρ를 α-spiral function of order ρ인 함수족이라 하자. 본 논문에서는 F_α,ρ의 closed convex hull의 극치점들을 찾아내고 이들을 이용하여 F_α,ρ에 속하는 함수 f(z)의 계수문제를 해결하고 |f(z)|와 |f (z)|의 상계를 구하였다. 그리고 F_α,ρ에 속하는 함수에 의하여 majorized 되는 함수와 subordinate 되는 함수의 계수문제들을 해결하였다. 또한 zf (z)이 함수족 F_α,ρ에 속하는 해석적이고 univalent한 함수 f(z)에 대하여 Re LEFT{ f(z) over z RIGHT}의 하계도 찾아내었다. ; Let F_α,ρ denote the class of α-spiral functions of order ρ. We obtain the extreme points of the closed convex hull of F_α,ρ. Using these extreme points of DF_α,ρ, we give short proofs for coefficient inequalities and distortion bounds for functions in F_α,ρ. We find the upper bounds for the coefficients of functions that are majorized by some function in F_α,ρ. Also, the coefficient estimates for functions which are subordinate to some function in F_α,ρ are given. Moreover, we establish the lower bound of Re LEFT{ f(z) over z RIGHT} where f(z) is regular, univalent in the unit disk for which zf (z)∈F_α,ρ.
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일반대학원 > 수학과 > Theses_Ph.D
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