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Proceedings of the American Mathematical Society

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The critical points of a typically-real function


Author: A. W. Goodman
Journal: Proc. Amer. Math. Soc. 38 (1973), 95-102
MSC: Primary 30A32
DOI: https://doi.org/10.1090/S0002-9939-1973-0313489-7
MathSciNet review: 0313489
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Abstract: The critical points of a typically-real function cannot lie too close to the real axis. By adding a mild restriction, we determine $ {D_k}$ the domain of variability of a $ k$th order critical point. Similar results are obtained for a $ k$th order branch point. We determine the domain of univalence for typically-real functions and propose a reasonable conjecture for the domain of $ k$-valence.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0313489-7
Keywords: Typically-real functions, critical points, branch points, subordination, Schwarz lemma, univalent functions, multivalent functions
Article copyright: © Copyright 1973 American Mathematical Society

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