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On the local extremum property of the Koebe function. (English) Zbl 1056.30019

Some year ago, Bshouty and Hengarter established necessary conditions in terms of Gâteaux-derivative for the local extremality of the Koebe mapping in extremal problems for univalent functions. In the paper, an analogue of the result for odd univalent functions is obtained. The technique is applied to study Robertson type inequalities and to investigate a conjecture of Bombieri.

MSC:

30C70 Extremal problems for conformal and quasiconformal mappings, variational methods
30C50 Coefficient problems for univalent and multivalent functions of one complex variable
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