Correspondence between spirallike functions and starlike functions

被引：8

作者：

Kim, Yong Chan ^{[2
]}

Sugawa, Toshiyuki ^{[1
]}

机构：

[1] Tohoku Univ, Grad Sch Informat Sci, Aoba Ku, Sendai, Miyagi 9808579, Japan

[2] Yeungnam Univ, Dept Math Educ, Kyongsan 712749, South Korea

来源：

MATHEMATISCHE NACHRICHTEN | 2012年 / 285卷 / 2-3期

关键词：

Spirallike (spiral-like) function; starlike function; Hardy space; logarithmic spiral; MSC (2010) 30C45; HARDY CLASS;

D O I：

10.1002/mana.201010020

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let ? be a real number with -p/2 < ? < p/2. In order to study ?-spirallike functions, it is natural to measure the angle according to ?-spirals. Thus we are led to the notion of ?-argument. This fits well the classical correspondence between ?-spirallike functions and starlike functions. Using this idea, we extend deep results of Pommerenke and Sheil-Small on starlike functions to spirallike functions. As an application, we solved a problem given by Hansen in 6.

引用

页码：322 / 331

页数：10

共 50 条

[1] Harmonic spirallike functions and harmonic strongly starlike functions
Xiu-Shuang Ma
Saminathan Ponnusamy
Toshiyuki Sugawa
Monatshefte für Mathematik, 2022, 199 : 363 - 375
[2] Harmonic spirallike functions and harmonic strongly starlike functions
Ma, Xiu-Shuang
Ponnusamy, Saminathan
Sugawa, Toshiyuki
MONATSHEFTE FUR MATHEMATIK, 2022, 199 (02): : 363 - 375
[3] Differential inequalities for spirallike and strongly starlike functions
Nak Eun Cho
Oh Sang Kwon
Young Jae Sim
Advances in Difference Equations, 2021
[4] Differential inequalities for spirallike and strongly starlike functions
Cho, Nak Eun
Kwon, Oh Sang
Sim, Young Jae
ADVANCES IN DIFFERENCE EQUATIONS, 2021, 2021 (01)
[5] Dynamics of spirallike functions
Elin, M
Goldvard, A
Reich, S
Shoikhet, D
COMPLEX ANALYSIS AND DYNAMICAL SYSTEMS: ISRAEL MATHEMATICAL CONFERENCE PROCEEDINGS, 2004, 364 : 41 - 57
[6] A NOTE ON SPIRALLIKE FUNCTIONS
Sim, Y. J.
Thomas, D. K.
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2022, 105 (01) : 117 - 123
[7] CLASS OF SPIRALLIKE FUNCTIONS
SILVIA, EM
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 20 (02): : A266 - A266
[8] STARLIKE FUNCTIONS
MCCARTY, CP
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 43 (02) : 361 - 366
[9] On harmonic meromorphic spirallike functions
Ali, Md Firoz
Pandit, Sushil
JOURNAL OF ANALYSIS, 2024, : 657 - 672
[10] ON STARLIKE FUNCTIONS
TWOMEY, JB
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 24 (01) : 95 - &

← 1 2 3 4 5 →