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On subclasses of analytic functions with respect to symmetrical points. (English) Zbl 1237.30003

Summary: In our present investigation, motivated by work of the second author, we define the class \(\mathcal R^s_k(b)\) of functions of bounded radius rotation of complex order \(b\) with respect to symmetrical points and learn some of its basic properties. We also apply this concept to define the class \(\mathcal H^s_k(\alpha, b, \delta)\). We study some interesting results, including arc length, coefficient difference, and sufficient conditions for univalence in this class.

MSC:

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