On power deformations of univalent functions

Title
On power deformations of univalent functions
Author(s)
김용찬Toshiyuki Sugawa[Toshiyuki Sugawa]
Issue Date
201208
Publisher
SPRINGER WIEN
Citation
MONATSHEFTE FUR MATHEMATIK, v.167, no.2, pp.231 - 240
Abstract
For an analytic function f (z) on the unit disk |z| < 1 with f (0) = f'(0) - 1 = 0 and f (z) not equal 0, 0 < |z| < 1, we consider the power deformation f (c) (z) = z(f (z)/z) (c) for a complex number c. We determine those values c for which the operator maps a specified class of univalent functions into the class of univalent functions. A little surprisingly, we will see that the set is described by the variability region of the quantity zf'(z)/ f (z), |z| < 1, for most of the classes that we consider in the present paper. As an unexpected by-product, we show boundedness of strongly spirallike functions.
URI
http://hdl.handle.net/YU.REPOSITORY/27476http://dx.doi.org/10.1007/s00605-011-0344-y
ISSN
0026-9255
Appears in Collections:
사범대학 > 수학교육과 > Articles
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