Neighborhoods of univalent functions

Mihai N. Pascu; Nicolae R. Pascu

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arXiv · 0910.5456

Neighborhoods of univalent functions

Mihai N. Pascu·Nicolae R. Pascu

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Abstract

The main result shows a small perturbation of a univalent function is again a univalent function, hence a univalent function has a neighborhood consisting entirely of univalent functions. For the particular choice of a linear function in the hypothesis of the main theorem, we obtain a corollary which is equivalent to the classical Noshiro-Warschawski-Wolff univalence criterion. We also present an application of the main result in terms of Taylor series, and we show that the hypothesis of our main result is sharp.

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Mihai N. Pascu, Nicolae R. Pascu. 2009-10-28. Neighborhoods of univalent functions. https://arxiv.org/abs/0910.5456

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