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Subclasses of harmonic mappings defined by convolution. (English) Zbl 1193.30007
Summary: Two new subclasses of harmonic univalent functions defined by convolution are introduced. The subclasses generate a number of known subclasses of harmonic mappings, and thus provide a unified treatment in the study of these subclasses. Sufficient coefficient conditions are obtained that are shown to be also necessary when the analytic parts of the harmonic functions have negative coefficients. Growth estimates and extreme points are also determined.

MSC:
30C45Special classes of univalent and multivalent functions
References:
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