Comprehensive family of $k$-uniformly harmonic starlike functions

B. A. Frasin, G. Murugusundaramoorthy

In this paper, we introduce a comprehensive family of k-uniformly 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. Further results on integral transforms are discussed. Consequently, many of our results are either extensions or new approaches to those corresponding previously known results.