Differential Inequalities and Criteria for Starlike and Univalent Functions

@inproceedings{Obradovic2006DifferentialIA,
  title={Differential Inequalities and Criteria for Starlike and Univalent Functions},
  author={Milutin Obradovic and S. Ponnusamy},
  year={2006}
}
The main aim of this paper is to use the method of differential subordination to obtain a number of sufficient conditions for a normalized analytic function to be univalent or starlike in the unit disc. In particular, we find a condition on β so that each normalized analytic function f satisfying the condition ∣∣∣1 + zf ′′(z) 2f ′(z) − zf ′(z) f(z) ∣∣∣ < β, z ∈ Δ implies that f is univalent or starlike in the unit disc. 
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