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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Two new extremal properties of the Koebe-function
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by R. Klouth and K.-J. Wirths PDF
Proc. Amer. Math. Soc. 80 (1980), 594-596 Request permission

Abstract:

Using essentially Löwner’s method the extremality of the Koebe-functions with respect to two coefficient problems for inverses of univalent functions is proved.
References
  • W. K. Hayman, Multivalent functions, Cambridge Tracts in Mathematics and Mathematical Physics, No. 48, Cambridge University Press, Cambridge, 1958. MR 0108586
  • Richard Klouth, Abschätzungen im Bereich der Schwarzschen Derivierten und gewisser Verallgemeinerungen, Bonner Mathematische Schriften, Nr. 82, Universität Bonn, Mathematisches Institut, Bonn, 1976 (German). Inaugural-Dissertation zur Erlangung des Doktorgrades der Hohen Mathematisch-Naturwissenschaftlichen Fakultät der Rheinischen Friedrich-Wilhelm-Universität Bonn, Bonn, 1975. MR 0492200
  • —, Abschätzungen verallgemeinerter Schwarzscher Derivierter für schlichte holomorphe Funktionen im Einheitskreis, Preprint des SFB 40 Theoretische Mathematik, Bonn, 1979.
  • Karl Löwner, Untersuchungen über schlichte konforme Abbildungen des Einheitskreises. I, Math. Ann. 89 (1923), no. 1-2, 103–121 (German). MR 1512136, DOI 10.1007/BF01448091
  • Christian Pommerenke, Univalent functions, Studia Mathematica/Mathematische Lehrbücher, Band XXV, Vandenhoeck & Ruprecht, Göttingen, 1975. With a chapter on quadratic differentials by Gerd Jensen. MR 0507768
  • Glenn Schober, Coefficient estimates for inverses of schlicht functions, Aspects of contemporary complex analysis (Proc. NATO Adv. Study Inst., Univ. Durham, Durham, 1979) Academic Press, London-New York, 1980, pp. 503–513. MR 623495
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 80 (1980), 594-596
  • MSC: Primary 30C50
  • DOI: https://doi.org/10.1090/S0002-9939-1980-0587934-X
  • MathSciNet review: 587934