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arXiv · 1203.3918

Radius problems associated with pre-Schwarzian and Schwarzian derivatives

S. Ponnusamy·S. K. Sahoo·T. Sugawa
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Abstract

Some of important univalence criteria for a non-constant meromorphic function $f(z)$ on the unit disk $\ID$ involve its pre-Schwarzian or Schwarzian derivative. We consider an appropriate norm for the pre-Schwarzian derivative, and discuss the problem of finding the largest possible $r\in (0,1)$ for which the pre-Schwarzian norm of the dilation $r^{-1}f(rz)$ is not greater than a prescribed number for normalized univalent functions $f(z)$ in the unit disk. Similar results concerning the Schwarzian derivative are also obtained

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S. Ponnusamy, S. K. Sahoo, T. Sugawa. 2012-03-18. Radius problems associated with pre-Schwarzian and Schwarzian derivatives. https://arxiv.org/abs/1203.3918

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