On a subclass of harmonic close-to-convex mappings

Let H denote the class of harmonic functions f defined in D:={zC:|z|<1}, and normalized by f(0)=0=fz(0)-1. In this paper, for 0, we consider the subclass WH0() of H, defined by For fWH0(), we prove the Clunie-Sheil-Small coefficient conjecture, and give some growth, convolution, and convex combination theorems. We also determine the value of r so that the partial sums of functions in WH0() are close-to-convex in |z| < r.