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Zbl 0985.30013
On the Fekete-Szeg\H{o} problem for alpha-quasi-convex functions.
(English)
[J] Tamkang J. Math. 31, No.4, 251-255 (2000). ISSN 0049-2930; ISSN 2073-9826/e

Let $Q_\alpha$ $(\alpha\ge 0)$ denote the class of normalized analytic alpha-quasi-convex functions $f$, defined in the unit disc, $D=\{z: |z|<1\}$, by the condition $$\text{Re}\left[ (1-\alpha){f'(z)\over g'(z)}+ \alpha{\bigl( zf'(z)\bigr)' \over g'(z)}\right] >0,$$ where $f(z)=z+ \sum^\infty_{n=2} a_nz^n$ and where $g(z)=z+ \sum^\infty_{n=2} b_nz^n$ is a convex univalent function in $D$. Sharp upper bounds are obtained for $|a_3-\mu a^2_2|$, when $\mu\ge 0$.
[Khalida Inayat Noor (Halifax)]
MSC 2000:
*30C45 Special classes of univalent and multivalent functions
30C50 Coefficient problems for univalent and multivalent functions

Keywords: quasi-convex functions; Fekete-Szeg\H{o} problem; upper bounds

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