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REGULAR FUNCTIONS WHICH IS TYPICALLY-REAL AND CONVEX IN THE DIREACTION OF THE IMAGINARY AXIS

Title
REGULAR FUNCTIONS WHICH IS TYPICALLY-REAL AND CONVEX IN THE DIREACTION OF THE IMAGINARY AXIS
Authors
문주란
Issue Date
1989
Department/Major
대학원 수학과
Keywords
REGULAR FUNCTIONTYPICALLY-REALCONVEXIMAGINARY AXIS수학
Publisher
이화여자대학교 대학원
Degree
Master
Abstract
In this thesis, we study some geometric properties concerning the class T of typically-real functions, and the class F of regular functions convex in the direction of the imaginary axis. In particular. we study that if g(z) = z+□ a_(n)z^(n) is typically-real functions, the length L(r) of the image curve Cr of □ = r under w = g(z) satisfies the inequality. ◁그림 삽입▷ (원문을 참조하세요) ;이 논문에서 Typically - real인 함수族 T와 허수축 방향으로 convex인 해석함수族 F에 관한 몇가지 기하학적 성질을 연구한다. 특히, 만일 g(z) = z + □a_(n)z^(n)가 typically - real인 함수라면 w = g(z)에 의한 |z| = r의 상인 곡선 Cr의 길이 L(r)은 다음 부둥식을 만족함을 보였다. L(r) ≤ r∫_(0)^(2π)|l+re^(iΘ)|/|l-re^(iΘ)|^(3)dΘ
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