Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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, vols. I and II, Mariner, Tampa, Florida, 1983. MR 704183 (85j:30035a)
  • [2] -, Convex curves of bounded type, University of Southern Florida Seminar Notes.
  • [3] M. S. Robertson, On the theory of univalent functions, Ann. of Math. 37 (1936), 374-408. MR 1503286
  • [4] E. Study, Konforme Abbildung Einfachzusammenhangender Bereiche, Teubner, Leipzig and Berlin, 1913.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30C45

Retrieve articles in all journals with MSC: 30C45

Additional Information

Keywords: Univalent functions, convex functions, coefficient bounds, Koebe domains
Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society