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  • NEIGHBOURHOODS OF UNIVALENT FUNCTIONS

  • Part of
  • MIHAI N. PASCU, NICOLAE R. PASCU
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 83 / Issue 2 / April 2011
    Published online by Cambridge University Press:
    14 September 2010, pp. 210-219
    Print publication:
    April 2011
    • Article
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  • The main result shows that a small perturbation of a univalent function is again a univalent function, hence a univalent function has a neighbourhood 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.