Neighborhoods of univalent functions

Details Neighborhoods of univalent functions Neighborhoods of univalent functions

2009-10-28

arxiv.org/abs/0910.5456v1

Mathematics

Complex Variables

9 pages, 1 figure

Scientific paper

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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