View : 356 Download: 0

Full metadata record

DC Field Value Language
dc.description.abstract본 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).-
dc.description.tableofcontents논문초록 -------------------------------------------------------------- ⅳ Ⅰ. Introduction ------------------------------------------------------ 1 Ⅱ. Weakly Starlike p-valent Functions -------------------------------- 8 Ⅲ. Weakly Close-to-Convex p-valent Functions ------------------------- 14 Ⅳ. Geometric Characterization of Weakly Close-to-convex p-valent Functions -------------------------------- 25 Ⅴ. Extremal Properties for The Classes ------------------------------- 32 References ------------------------------------------------------------ 40 Abstract -------------------------------------------------------------- 42-
dc.format.extent1083680 bytes-
dc.publisher이화여자대학교 대학원-
dc.titleWeakly starlike and weakly close-to-convex p-valent functions-
dc.typeDoctoral Thesis-
dc.identifier.major대학원 수학과- 2-
Appears in Collections:
일반대학원 > 수학과 > Theses_Ph.D
Files in This Item:
There are no files associated with this item.
RIS (EndNote)
XLS (Excel)


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.