Abstract
Let λ be a real number with -π/2 < λ < π/2. In order to study λ-spirallike functions, it is natural to measure the angle according to λ-spirals. Thus we are led to the notion of λ-argument. This fits well the classical correspondence between λ-spirallike functions and starlike functions. Using this idea, we extend deep results of Pommerenke and Sheil-Small on starlike functions to spirallike functions. As an application, we solved a problem given by Hansen in 6.
Original language | English |
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Pages (from-to) | 322-331 |
Number of pages | 10 |
Journal | Mathematische Nachrichten |
Volume | 285 |
Issue number | 2-3 |
DOIs | |
Publication status | Published - 2012 Feb 1 |
Keywords
- Hardy space
- Logarithmic spiral
- Spirallike (spiral-like) function
- Starlike function
ASJC Scopus subject areas
- Mathematics(all)