Inclusion and neighborhood properties for certain classes of multivalently analytic functions associated with the convolution structure. (English) Zbl 1131.30006

Summary: Making use of the familiar convolution structure of analytic functions, in this paper we introduce and investigate two new subclasses of multivalently analytic functions of complex order. Among the various results obtained here for each of these function classes, we derive the coefficient bounds and coefficient inequalities, and inclusion and neighborhood properties, involving multivalently analytic functions belonging to the function classes introduced here.


30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30A10 Inequalities in the complex plane
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