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Zbl 1058.30015
Kamali, Muhammet; Srivastava, H.M.
A sufficient condition for starlikeness of analytic functions of Koebe type. (English)
[J] JIPAM, J. Inequal. Pure Appl. Math. 5, No. 3, Paper No. 57, 8 p., electronic only (2004). ISSN 1443-5756/e

The authors use the Jack Lemma and a result involving differential inequalities due to Miller and Mocanu to obtain sufficient conditions over the real part of $$\alpha z^2 \frac{f_b''(z)}{f_b(z)}+\frac{zf'_b(z)}{f_b(z)}$$ that implies starlikeness of a Koebe type function $$f_b(z)=\frac{z}{(1-z^n)^b},$$ $b\ge0,$ $n=1,2,3,\ldots.$
[Nikola Tuneski (Skopje)]

MSC 2000:: *30C45 Special classes of univalent and multivalent functions
30A10 Inequalities in the complex domain
30C80 Maximum principle, etc. (one complex variable)

Keywords: Koebe type function; starlike function; sufficient condition; differential inequalities; Jack Lemma

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