We consider the class SH(D,W ) of complex functions f which are univalent, harmonic, sense preserving on a simple connected domain D\neq {\Bbb C} \ containing the origin, satisfy f(0)=a0, f\bar z(0)=0a,\ a\in {\Bbb R}\}. In particularly, we describe the closure \overline{SH(D,W )} of SH(D,W ) and characterize its extreme points, as well as sharp estimates for coefficients and distortion theorems.

We consider the class SH(D,W ) of complex functions f which are univalent, harmonic, sense preserving on a simple connected domain D\neq {\Bbb C} \ containing the origin, satisfy f(0)=a0, f\bar z(0)=0a,\ a\in {\Bbb R}\}. In particularly, we describe the closure \overline{SH(D,W )} of SH(D,W ) and characterize its extreme points, as well as sharp estimates for coefficients and distortion theorems.