# Variability regions of close-to-convex functions

Takao Kato; Toshiyuki Sugawa; Li-Mei Wang

Annales Polonici Mathematici (2014)

- Volume: 111, Issue: 1, page 89-105
- ISSN: 0066-2216

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topTakao Kato, Toshiyuki Sugawa, and Li-Mei Wang. "Variability regions of close-to-convex functions." Annales Polonici Mathematici 111.1 (2014): 89-105. <http://eudml.org/doc/280289>.

@article{TakaoKato2014,

abstract = {M. Biernacki gave in 1936 concrete forms of the variability regions of z/f(z) and zf'(z)/f(z) of close-to-convex functions f for a fixed z with |z|<1. The forms are, however, not necessarily convenient to determine the shape of the full variability region of zf'(z)/f(z) over all close-to-convex functions f and all points z with |z|<1. We propose a couple of other forms of the variability regions and see that the full variability region of zf'(z)/f(z) is indeed the complex plane minus the origin. We also apply them to study the variability regions of log[z/f(z)] and log[zf'(z)/f(z)].},

author = {Takao Kato, Toshiyuki Sugawa, Li-Mei Wang},

journal = {Annales Polonici Mathematici},

keywords = {close-to-convex functions; variability region; linearly accessible domains},

language = {eng},

number = {1},

pages = {89-105},

title = {Variability regions of close-to-convex functions},

url = {http://eudml.org/doc/280289},

volume = {111},

year = {2014},

}

TY - JOUR

AU - Takao Kato

AU - Toshiyuki Sugawa

AU - Li-Mei Wang

TI - Variability regions of close-to-convex functions

JO - Annales Polonici Mathematici

PY - 2014

VL - 111

IS - 1

SP - 89

EP - 105

AB - M. Biernacki gave in 1936 concrete forms of the variability regions of z/f(z) and zf'(z)/f(z) of close-to-convex functions f for a fixed z with |z|<1. The forms are, however, not necessarily convenient to determine the shape of the full variability region of zf'(z)/f(z) over all close-to-convex functions f and all points z with |z|<1. We propose a couple of other forms of the variability regions and see that the full variability region of zf'(z)/f(z) is indeed the complex plane minus the origin. We also apply them to study the variability regions of log[z/f(z)] and log[zf'(z)/f(z)].

LA - eng

KW - close-to-convex functions; variability region; linearly accessible domains

UR - http://eudml.org/doc/280289

ER -

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