  In this paper, we first prove relation between analytic and co-analytic part
of the class harmonic univalent functions S_H(S):={f = h+\overline g|h is
element of S} by means of second dilatation is constant. Next, we verify the
coefficient conjecture of Clunie and Sheil-Small for class of harmonic
univalent functions. Finally, we obtain distortion bounds of this class.

Complex Variables