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Comprehensive family of harmonic univalent functions. (English) Zbl 1104.30007
Summary: We introduce a comprehensive family of harmonic univalent functions which contains various well-known classes of harmonic univalent functions as well as many new ones. Coefficient bounds, distortion bounds, extreme points, convolution conditions, and convex combination are determined for functions in this family. Consequently, many of our results are either extensions or new approaches to those corresponding previously known results.

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