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

[31] ON MEROMORPHIC STARLIKE FUNCTIONS
POMMERENKE, C
PACIFIC JOURNAL OF MATHEMATICS, 1963, 13 (01) : 221 - &
[32] A CLASS OF STARLIKE FUNCTIONS
LIVINGSTON, AE
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1993, 23 (01) : 289 - 307
[33] On a Subclass of Starlike Functions
Maslina Darus
Saqib Hussain
Mohsan Raza
Janusz Sokół
Results in Mathematics, 2018, 73
[34] MEROMORPHIC STARLIKE FUNCTIONS
TWOMEY, JB
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1971, 4 (DEC): : 231 - &
[35] ON THE THEORY OF STARLIKE FUNCTIONS
BUSOVSKAYA, OA
GORYAINOV, VV
DOPOVIDI AKADEMII NAUK UKRAINSKOI RSR SERIYA A-FIZIKO-MATEMATICHNI TA TECHNICHNI NAUKI, 1981, (02): : 6 - 8
[36] STARLIKE SYMMETRICAL FUNCTIONS
Al Sarari, Fuad S.
TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, 2020, 10 (04): : 1145 - 1154
[37] On multivalent starlike functions
Nunokawa, Mamoru
Sokol, Janusz
Tuneski, Nikola
Jolevska-Tuneska, Biljana
STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, 2019, 64 (01): : 91 - 102
[38] On a Subclass of Starlike Functions
Mohamed, Norlyda
Mohamad, Daud
Soh, Shaharuddin C.
INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS & STATISTICS, 2015, 53 (04): : 131 - 136
[39] Unified Approach to Starlike and Convex Functions Involving Convolution Between Analytic Functions
Syed Zakar Hussain Bukhari
Janusz Sokol
Sidra Zafar
Results in Mathematics, 2018, 73
[40] COEFFICIENTS OF STARLIKE FUNCTIONS
HOLLAND, F
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 33 (02) : 463 - &

← 1 2 3 4 5 →