Premium
Regions of variability for convex functions
Author(s) -
Yanagihara Hiroshi
Publication year - 2006
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310449
Subject(s) - mathematics , regular polygon , class (philosophy) , combinatorics , convex function , unit (ring theory) , pure mathematics , geometry , computer science , mathematics education , artificial intelligence
Let be the class of convex univalent functions f in the unit disc normalized by f (0) = f ′(0) – 1 = 0. For z 0 ∈ and | λ | ≤ 1 we shall determine explicitly the regions of variability {log f ′( z 0 ): f ∈ , f ″(0) = 2 λ }. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)