Variability regions of close-to-convex functions

Takao Kato, Toshiyuki Sugawa, Li Mei Wang

研究成果: Article査読

抄録

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)].

本文言語English
ページ(範囲)89-105
ページ数17
ジャーナルAnnales Polonici Mathematici
111
1
DOI
出版ステータスPublished - 2014

ASJC Scopus subject areas

  • Mathematics(all)

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