On power deformations of univalent functions

Yong Chan Kim, Toshiyuki Sugawa

研究成果: Article査読

4 被引用数 (Scopus)

抄録

For an analytic function f (z) on the unit disk {pipe}z{pipe} < 1 with f (0) = f′(0) - 1 = 0 and f (z) ≠ 0, 0 < {pipe}z{pipe} < 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 → f c 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), {pipe}z{pipe} < 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.

本文言語English
ページ(範囲)231-240
ページ数10
ジャーナルMonatshefte fur Mathematik
167
2
DOI
出版ステータスPublished - 2012 8

ASJC Scopus subject areas

  • 数学 (全般)

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