A class of univalent harmonic functions defined by multiplier transformation. (English) Zbl 1289.30076
Summary: In this paper, we define subclasses \(RS_H(k,\lambda,\gamma)\) and \(RS_{\overline H}(k,\lambda,\gamma)\) of univalent harmonic functions by using multiplier transformation \(I(k,\lambda)\). Certain coefficient conditions and extreme points for the above classes are obtained. We also discuss convolution properties of the functions from the class \(RS_{\overline H}(k,\lambda,\gamma)\).
MSC:
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
| 30C55 | General theory of univalent and multivalent functions of one complex variable |
| 31A05 | Harmonic, subharmonic, superharmonic functions in two dimensions |
