Boundedness, univalence and quasiconformal extension of Robertson functions

Details Boundedness, univalence and quasiconformal extension of Robertson functions Boundedness, univalence and quasiconformal extension of Robertson functions

2010-03-10

arxiv.org/abs/1003.2019v2

Mathematics

Complex Variables

8 pages

Scientific paper

This article contains several results for \lambda-Robertson functions, i.e., analytic functions $f$ defined on the unit disk $D$ satisfying $f(0) = f'(0)-1=0$ and $Re e^{-i\lambda} {1+zf"(z)/f'(z)} > 0$ in $D$, where $\lambda \epsilon (-\pi/2,\pi/2)$. We will discuss about conditions for boundedness and quasiconformal extension of Robertson functions. In the last section we provide another proof of univalence for Robertson functions by using the theory of L\"owner chains.

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