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Subclasses of meromorphic functions associated with convolution. (English) Zbl 1176.30044

Summary: Several subclasses of meromorphic functions in the unit disk are introduced by means of convolution with a given fixed meromorphic function. Subjecting each convoluted-derived function in the class to be subordinated to a given normalized convex function with positive real part, these subclasses extend the classical subclasses of meromorphic starlikeness, convexity, close-to-convexity, and quasi-convexity. Class relations, as well as inclusion and convolution properties of these subclasses are investigated.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination
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