Let be a fixed univalent and sense-preserving harmonic mapping which is convex in the real direction but is not starlike in the unit disk . The convolution of with other harmonic mappings, eg. half-plane mappings, is not necessarily univalent in . In this paper, under suitable restriction on the dilatation of , we show that the convolutions of with certain slanted half-plane harmonic mappings are necessarily convex in a direction. In addition, we consider a fixed harmonic mapping and with the dilatation , where denotes the class of asymmetric vertical strip mappings. We find the relationship b...
