Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.author | 박영옥 | - |
dc.creator | 박영옥 | - |
dc.date.accessioned | 2016-08-26T02:08:44Z | - |
dc.date.available | 2016-08-26T02:08:44Z | - |
dc.date.issued | 1997 | - |
dc.identifier.other | OAK-000000000770 | - |
dc.identifier.uri | https://dspace.ewha.ac.kr/handle/2015.oak/192063 | - |
dc.identifier.uri | http://dcollection.ewha.ac.kr/jsp/common/DcLoOrgPer.jsp?sItemId=000000000770 | - |
dc.description.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. | - |
dc.description.tableofcontents | Table of contents --------------------------------------------------- ⅲ Abstract ------------------------------------------------------------ ⅴ Ⅰ. Introduction ---------------------------------------------------- 1 Ⅱ. Geometric properties for the class G_k(β) ---------------------- 5 2.1 Geometric interpretation --------------------------------------- 5 2.2 Radius of convexity -------------------------------------------- 8 2.3 Distortion and covering theorem -------------------------------- 9 Ⅲ. Coefficient estimates and invariance property for the class G_k(β) ----------------------------------------------------------------- 13 3.1 Coefficient estimates ------------------------------------------ 13 3.2 Invariance property -------------------------------------------- 19 3.3 Boundary behavior ---------------------------------------------- 23 Ⅳ. Geometric properties for the class H_k(β) ---------------------- 27 4.1 Geometric interpretation --------------------------------------- 27 4.2 Coefficient estimates ------------------------------------------ 31 4.3 Distortion and radius of starlikeness -------------------------- 32 Ⅴ. The subclass of G_k(1) described by subordination --------------- 34 5.1 Distortion and rotation theorem for G_k[A,B] ------------------- 34 5.2 Coefficient inequalities for G_k[A,B] -------------------------- 36 5.3 Invariance property for G_k[A,B] ------------------------------- 37 5.4 Inclusion relation for G_k[A,B] -------------------------------- 39 References ---------------------------------------------------------- 41 논문초록 ------------------------------------------------------------ 43 | - |
dc.format | application/pdf | - |
dc.format.extent | 1253528 bytes | - |
dc.language | eng | - |
dc.publisher | 이화여자대학교 대학원 | - |
dc.title | A class of holomorphic functions related to the functions with bounded boundary rotation | - |
dc.type | Doctoral Thesis | - |
dc.identifier.thesisdegree | Doctor | - |
dc.identifier.major | 대학원 수학과 | - |
dc.date.awarded | 1997. 8 | - |