Variability regions of close-to-convex functions

Takao 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 -