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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On analytic injective matrix functions


Authors: D. Bshouty and W. Hengartner
Journal: Proc. Amer. Math. Soc. 88 (1983), 459-463
MSC: Primary 30C55; Secondary 15A57
MathSciNet review: 699414
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Abstract: An ingenious generalization of univalent functions of one complex variable into matrix functions was introduced by B. Schwarz, along with two conjectures corresponding to the first coefficient problem and the second coefficient problem for the traditional classes $ \Sigma $ and $ S$, respectively. We exhibit two counterexamples for these conjectures.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0699414-4
Keywords: Univalent functions, injective matrix functions
Article copyright: © Copyright 1983 American Mathematical Society