Geodesic
On an extremal problem
Mathematica Bohemica, Tome 120 (1995) no. 2, pp. 113-124

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MR Zbl
Let $S$ denote the class of functions $f(z) = z + a_2z^2 + a_3z^3 + \ldots$ univalent and holomorphic in the unit disc $\varDelta= \{z |z| 1\}$. In the paper we obtain a sharp estimate of the functional $|a_3 - \alpha a^2_2| + \alpha|a_2|^2$ in the class $S$ for an arbitrary $\alpha\in\Bbb R$.
Let $S$ denote the class of functions $f(z) = z + a_2z^2 + a_3z^3 + \ldots$ univalent and holomorphic in the unit disc $\varDelta= \{z |z| 1\}$. In the paper we obtain a sharp estimate of the functional $|a_3 - \alpha a^2_2| + \alpha|a_2|^2$ in the class $S$ for an arbitrary $\alpha\in\Bbb R$.
DOI : 10.21136/MB.1995.126223
Classification : 30C50, 30C70
Keywords: coefficient problems; Koebe function; univalent function 
Zyskowska, Krystyna. On an extremal problem. Mathematica Bohemica, Tome 120 (1995) no. 2, pp. 113-124. doi: 10.21136/MB.1995.126223
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