Some properties of harmonic functions defined by convolution. (English) Zbl 1188.30010

Dixit, Kaushal Kishor; Porwal, Saurabh

Kyungpook Math. J. 49, No. 4, 751-761 (2009).

Summary: We introduce and study a comprehensive family of harmonic univalent functions which contains various well-known classes of harmonic univalent functions as well as many new ones. Also, we improve some results obtained by B. A. Frasin [SUT J. Math. 42, No. 1, 145–155 (2006; Zbl 1104.30007)] and obtain coefficient bounds, distortion bounds, and extreme points. Convolution conditions and convex combinations are also determined for functions in this family. It is worth mentioning that many of our results are either extensions or new approaches to corresponding previously known results.

MSC:

30C45	Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C50	Coefficient problems for univalent and multivalent functions of one complex variable

Keywords:

harmonic function; univalent analytic function