On Convolution of Harmonic Mappings

For j = 1, 2, let the sense-preserving locally univalent harmonic mappings F-j = H-j + (G(j)) over bar on D := {z is an element of C : |z| < 1} be such that <(F-j((z) over bar))over bar> = F-j(z) and the mappings z(H-j + G(j))' are either odd starlike or starlike of order 1/2. It is shown that the convolution F-1 * F-2 of F-1 and F-2 is directional convex univalent mapping if it is locally univalent sense-preserving. Also, some examples are given where F-1 * F-2 is locally univalent sense-preserving.