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A class of holomorphic functions related to the functions with bounded boundary rotation

Title
A class of holomorphic functions related to the functions with bounded boundary rotation
Authors
박영옥
Issue Date
1997
Department/Major
대학원 수학과
Publisher
이화여자대학교 대학원
Degree
Doctor
Abstract
복소해석적 함수 f(z)에 대하여, 만약 convex 함수 h(z)가 있어서 f (z) βπ |arg ----- |≤--- , (z ∈ E) h (z) 2 를 만족한다면, 그와같은 함수 f(z)를 단위원 내에서 strongly close-to-convex 함수라 부른다. 우리는 위에서 사용한 함수 h(z)대신 bounded boundary rotation 함수 g(z)를 사용함으로써 strongly close-to-convex 함수를 일반화시키고, 새로운 복소해석함수족 G_k(β), H_k(β) 그리고 G_k[A,B]를 구성한다. 본 논문에서는 함수족 G_k(β), H_k(β) 그리고 G_k[A,B]에 대하여 계수문제, convex의 반경문제, 불변성 문제, distortion 정리, covering 정리 등을 포함한 여러가지 문제를 풀어본다. ; A holomorphic function f(z)is said to be strongly close-to-convex in E if there exists a convex function h(z) such that f (z) βπ |arg ----- |≤--- , (z ∈ E) h (z) 2 We generalize the definition of strongly close-to-convex functions by using the functions g(z) of bounded boundary rotation instead of h(z) above and construct new classes of holomorphic functions G_k(ß),H_k(β) and G_k[A,B]. We find several results for the classes G_k(β),H_k(β) and G_k[A,B] including coefficient estimates, radius of convexity problem, invariance property, distortion theorem and covering theorem, etc.
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