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On certain sufficient conditions for starlikeness. (English) Zbl 0954.30003
The author makes use of the method of differential subordination due to S. Miller and P. T. Mocanu [Mich. Math. J. 28, 157-172 (1981; Zbl 0456.30022)] to obtain some sufficient conditions for starlikeness. A typical result is as follows: If \(f(z)=z+ \sum^\infty_{k=2} a_kz^k\) for \(|z|<1\) and \[ f(z)f''(z) \bigl(f'(z) \bigr)^{-2} \prec 2-2(1-z)^2 \] holds the unit disk, then \(f\) is starlike univalent.

MSC:
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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