On an extremal problem

Abstract: 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 $\alpha\in\Bbb R$.

Keywords: univalent function, coefficient problem

Classification (MSC91): 30C50

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