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The domain of univalence of certain families of rational functions

Author: A. W. Goodman
Journal: Proc. Amer. Math. Soc. 66 (1977), 85-90
MSC: Primary 30A32
MathSciNet review: 0584957
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Abstract: The Čakalov-Distler Theorem gives the domain of univalence for the family of all rational functions for which all the poles are simple, all the poles lie in a prescribed convex set, and all have positive residue. Here we extend this theorem to allow simple poles with negative residues. We include several open problems.

References [Enhancements On Off] (What's this?)

  • [1] L. Čakalov, Sur une classe de fonctions analytiques univalentes, C. R. Acad. Sci. Paris 242 (1956), 437-439. MR 0075300 (17:724f)
  • [2] -, Sur les domaines d'univalence de certaines classes de fonctions analytiques, B"lgar. Akad. Nauk Izv. Mat. Inst. 4 (1960), No. 2, 43-55. (Bulgarian, Russian and French summaries). MR 0123700 (23:A1022)
  • [3] R. J. Distler, The domain of univalence of certain classes of meromorphic functions, Proc. Amer. Math. Soc. 15 (1964), 923-928. MR 0167610 (29:4882)
  • [4] S. Lameier, On domains of univalence of certain meromorphic functions, Master's Thesis, University of Cincinnati, Cincinnati, Ohio.

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Keywords: Univalent functions, rational functions, domain of univalence, Čakalov-Distler Theorem
Article copyright: © Copyright 1977 American Mathematical Society

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