The Alexander transform of a spirallike function

Yong Chan Kim; Toshiyuki Sugawa

doi:10.1016/j.jmaa.2006.01.077

The Alexander transform of a spirallike function

Yong Chan Kim, Toshiyuki Sugawa

INF - Computer and Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

We show that the Alexander transform of a β-spirallike function is univalent when cos β ≤ 1 / 2, which settles the problem posed by Robertson. We also solved a problem considered by Y.J. Kim and Merkes.

Original language	English
Pages (from-to)	608-611
Number of pages	4
Journal	Journal of Mathematical Analysis and Applications
Volume	325
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2006.01.077
Publication status	Published - 2007 Jan 1

Keywords

Integral transform
Spirallike function
Univalent function

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2006.01.077

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title = "The Alexander transform of a spirallike function",

abstract = "We show that the Alexander transform of a β-spirallike function is univalent when cos β ≤ 1 / 2, which settles the problem posed by Robertson. We also solved a problem considered by Y.J. Kim and Merkes.",

keywords = "Integral transform, Spirallike function, Univalent function",

author = "Kim, {Yong Chan} and Toshiyuki Sugawa",

note = "Funding Information: * Corresponding author. E-mail addresses: kimyc@yumail.ac.kr (Y.C. Kim), sugawa@math.sci.hiroshima-u.ac.jp (T. Sugawa). 1 The second author was supported in part by MEXT Grant-in-Aid for Scientific Research (B), 17340039.",

year = "2007",

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day = "1",

doi = "10.1016/j.jmaa.2006.01.077",

language = "English",

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pages = "608--611",

journal = "Journal of Mathematical Analysis and Applications",

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T1 - The Alexander transform of a spirallike function

AU - Kim, Yong Chan

AU - Sugawa, Toshiyuki

N1 - Funding Information: * Corresponding author. E-mail addresses: kimyc@yumail.ac.kr (Y.C. Kim), sugawa@math.sci.hiroshima-u.ac.jp (T. Sugawa). 1 The second author was supported in part by MEXT Grant-in-Aid for Scientific Research (B), 17340039.

PY - 2007/1/1

Y1 - 2007/1/1

N2 - We show that the Alexander transform of a β-spirallike function is univalent when cos β ≤ 1 / 2, which settles the problem posed by Robertson. We also solved a problem considered by Y.J. Kim and Merkes.

AB - We show that the Alexander transform of a β-spirallike function is univalent when cos β ≤ 1 / 2, which settles the problem posed by Robertson. We also solved a problem considered by Y.J. Kim and Merkes.

KW - Integral transform

KW - Spirallike function

KW - Univalent function

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DO - 10.1016/j.jmaa.2006.01.077

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AN - SCOPUS:33750319169

VL - 325

SP - 608

EP - 611

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

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