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Weakly starlike and weakly close-to-convex p-valent functions

Title
Weakly starlike and weakly close-to-convex p-valent functions
Authors
홍혜성
Issue Date
2002
Department/Major
대학원 수학과
Publisher
이화여자대학교 대학원
Degree
Doctor
Abstract
본 논문은 Hummel이 연구한 Starlike 다엽함수족 S^* (p)의 알려진 여러가지 성질들을 공부하여 미약 Starlike p-가함수족 S^*`_w (p)를 구성하고, 그것을 이용하여 Livingston이 정의한 Close-to-convex 다엽함수족 C(p)를 확장하는 6가지 방법을 연구하고, 그들의 포함관계를 증명하였다. 또한 Kaplan이 단엽 Close-to-convex 함수족 C(1)을 위해 발견한 기하학적 특성을, 새로 구성한 미약 Close-to-convex p-가 함수족 C_w (p)에도 적용되도록 조건을 첨가하여 새로운 정리를 유도하고, 이를 증명하였다. 한편, 미약 Close-to-convex p-가 함수족 C_w (p)에 uniform convergence에 의해 만들어진 위상을 줌으로써 C_w (p)가 compact family가 됨을 확인하고, S^*`_w (p) ⊂ C_w (p) 인 미약 starlike p-가 함수족 S^*`_w (p)의 극치문제와 Goodman Conjecture의 성립을 뒷받침하는 C_w (p)의 계수문제를 서술하고, 이를 증명하였다. ; In this dissertation we study three kinds of extended version of starlike p-valent functions in S^* (p) which was initiated by Hummel and then we prove they are equivalent each other. Moreover, we investigate several ways to define Weakly Close-to-convex p-valent functions in terms of weakly starlike p-valent functions in S^*`_w (p) in order to expand the Livingston s class C(p) and we prove their inclusion relations. In particular, we were able to derive a geometric characterization of the function f(z) ∈ C_w (p) by using lemmas given by Kaplan and Livingston. Furthermore, by giving the uniform convergence topology in the class C_w (p) with S^*`_w (p) ⊂ C_w (p), we obtain extremal properties for the classes S^*`_w (p) and C_w (p).
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일반대학원 > 수학과 > Theses_Ph.D
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