Generalized bounded boundary turning functions. (English) Zbl 1119.30008
Summary: For a Jordan domain with smooth boundary, the boundary rotation \(\theta\) is defined as the total variation of the direction angle of the tangent to the boundary curve under a complete circuit. The domain is said to have bounded turning or rotation if \(\theta < \infty\) and the functions under such mappings are called functions of bounded boundary turning or rotation. We define a generalization of this concept and examine some of its properties. A few open problems are also stated for further explorations.
MSC:
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
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