Variability regions of close-to-convex functions

• Autorzy: Takao Kato , Toshiyuki Sugawa , Li-Mei Wang
• Języki publikacji: EN

Abstrakty

EN

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)].

Kategorie tematyczne

• 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
• 30C75: Extremal problems for conformal and quasiconformal mappings, other methods

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2014
• Tom: 111
• Numer: 1
• Strony: 89-105

Daty

wydano

2014

Twórcy

autor

Takao Kato

• Graduate School of Science and Engineering, Yamaguchi University, Yoshida, Yamaguchi 753-8512, Japan

autor

Toshiyuki Sugawa

• Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai 980-8579, Japan

autor

Li-Mei Wang

• School of Statistics, University of International Business and Economics, No. 10, Huixin Dongjie, Chaoyang District, Beijing 100009, China

Identyfikatory

DOI

10.4064/ap111-1-7