  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.
