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A note on the class of functions with bounded turning. (English) Zbl 1237.30004

Summary: We consider subclasses of functions with bounded turning for normalized analytic functions in the unit disk. The geometric representation is introduced, some subordination relations are suggested, and the upper bound of the pre-Schwarzian norm for these functions is computed. Moreover, by employing Jack’s lemma, we obtain a convex class in the class of functions of bounded turning and relations with other classes are posed.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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