In this note we prove the Bieberbach conjecture for some classes of quaternionic functions, including quaternionic slice regular functions with specific geometric properties such as starlike and convex functions. At the same time, we investigate some interesting properties related to the concepts of starlikeness for these quaternionic slice regular functions. Furthermore, we introduce and obtain generalizations and results for the class of quaternionic Carath´eodory functions, such as a version of Rogosinski’s Theorem over the quaternions.
A note on the Bieberbach conjecture for some classes of slice regular functions / A. Gori, F. Vlacci. - In: RENDICONTI DELL'ISTITUTO DI MATEMATICA DELL'UNIVERSITÀ DI TRIESTE. - ISSN 0049-4704. - 53:19(2021), pp. 1-16. [10.13137/2464-8728/33302]
A note on the Bieberbach conjecture for some classes of slice regular functions
A. Gori;
2021
Abstract
In this note we prove the Bieberbach conjecture for some classes of quaternionic functions, including quaternionic slice regular functions with specific geometric properties such as starlike and convex functions. At the same time, we investigate some interesting properties related to the concepts of starlikeness for these quaternionic slice regular functions. Furthermore, we introduce and obtain generalizations and results for the class of quaternionic Carath´eodory functions, such as a version of Rogosinski’s Theorem over the quaternions.File | Dimensione | Formato | |
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