Covering problems for functions \(n\)-fold symmetric and convex in the direction of the real axis. (English) Zbl 1296.30019
Summary: Let \(\mathcal{F}\) denote the class of all functions univalent in the unit disk and convex in the direction of the real axis. In the paper we discuss the functions of the class \(\mathcal{F}\) which are \(n\)-fold symmetric, where \(n\) is positive even integer. For the class of such functions we find the Koebe set as well as the covering set, i.e. \(\bigcap_{f\in\mathcal{F}}f(\Delta )\) and \(\bigcup_{f\in\mathcal{F}}f(\Delta )\). Moreover, the Koebe constant and the covering constant are obtained.
MSC:
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
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