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Generalized \(q\)-starlike functions. (English) Zbl 1413.30077

Summary: In this paper, we introduce a new concept of \(q\)-bounded radius rotation and define the class \(R^*_m(q),m\geq 2,q\in (0,1).\) The class \(R^*_2(q)\) coincides with \(S^*_q\) which consists of \(q\)-starlike functions defined in the open unit disc. Distortion theorems, coefficient result and radius problem are studied. Relevant connections to various known results are pointed out.

MSC:

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