Convex functions of bounded type
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- by A. W. Goodman PDF
- Proc. Amer. Math. Soc. 92 (1984), 541-546 Request permission
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 $\left | {f(z)} \right |$. We also mention a few of the many questions that can be asked about this new class of univalent functions.References
- A. W. Goodman, Univalent functions. Vol. I, Mariner Publishing Co., Inc., Tampa, FL, 1983. MR 704183 —, Convex curves of bounded type, University of Southern Florida Seminar Notes.
- Malcolm I. S. Robertson, On the theory of univalent functions, Ann. of Math. (2) 37 (1936), no. 2, 374–408. MR 1503286, DOI 10.2307/1968451 E. Study, Konforme Abbildung Einfachzusammenhangender Bereiche, Teubner, Leipzig and Berlin, 1913.
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 92 (1984), 541-546
- MSC: Primary 30C45
- DOI: https://doi.org/10.1090/S0002-9939-1984-0760942-5
- MathSciNet review: 760942