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Coefficients of parabolic starlike functions of order \(\rho\). (English) Zbl 0874.30007

Ali, Rosihan M. (ed.) et al., Computational methods and function theory 1994. Proceedings of the conference, Penang, Malaysia, March 21–25, 1994. Singapore: World Scientific. Ser. Approx. Decompos. 5, 23-36 (1995).
The authors consider starlike functions \(f(z)= z+\sum^\infty_{k=2} a_kz^k\), for which the image of the unit disc under the mapping \({zf'(z) \over f(z)}\) lies in certain parabolic regions of the right half plane. Using new and old inequalities for functions with positive real part they get sharp bounds for \(|a_k |\), \(k=2,3,4\) and for the first four Taylor coefficient of the inverse of such function \(f\). These problems have to be seen in connection with the coefficient problem for uniformly convex functions.
For the entire collection see [Zbl 0863.00033].

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C50 Coefficient problems for univalent and multivalent functions of one complex variable
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