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Proceedings of the American Mathematical Society

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

 

 

Convex functions of bounded type


Author: A. W. Goodman
Journal: Proc. Amer. Math. Soc. 92 (1984), 541-546
MSC: Primary 30C45
MathSciNet review: 760942
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Abstract: We introduce a new class of normalized functions univalent and convex in the unit disk. These are called convex of bounded type and the set is denoted by $ CV({R_1},{R_2})$. For this set we find the Koebe domain, a coefficient bound, and a bound for $ \left\vert {f(z)} \right\vert$. We also mention a few of the many questions that can be asked about this new class of univalent functions.


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

  • [1] A. W. Goodman, Univalent functions. Vol. I, Mariner Publishing Co., Inc., Tampa, FL, 1983. MR 704183
  • [2] -, Convex curves of bounded type, University of Southern Florida Seminar Notes.
  • [3] Malcolm I. S. Robertson, On the theory of univalent functions, Ann. of Math. (2) 37 (1936), no. 2, 374–408. MR 1503286, 10.2307/1968451
  • [4] E. Study, Konforme Abbildung Einfachzusammenhangender Bereiche, Teubner, Leipzig and Berlin, 1913.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0760942-5
Keywords: Univalent functions, convex functions, coefficient bounds, Koebe domains
Article copyright: © Copyright 1984 American Mathematical Society