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On the local extremum property of the Koebe function

Published online by Cambridge University Press:  18 February 2004

DMITRI PROKHOROV  and
OLIVER ROTH
DMITRI PROKHOROV
Affiliation:
Faculty of Mathematics and Mechanics, Saratov State University, Astrakhanskaya, 83, 410071 Saratov, Russia.
OLIVER ROTH
Affiliation:
Mathematisches Institut, Universität Würzburg, D-97074 Würzburg, Germany.
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Abstract

We discuss and compare several necessary criteria for the local extremality of the Koebe mapping in extremal problems for univalent functions. These criteria are applied to study Robertson type inequalities and also to investigate a conjecture of Bombieri.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 136 , Issue 2 , March 2004 , pp. 301 - 312
Copyright
2004 Cambridge Philosophical Society

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