Stability of convolution and dual sets for the class of k-uniformly convex and k-starlike functions

Let k-UCV denote the class of k-uniformly convex functions and let k-ST be related class of k- starlike functions. Also, let f*g denote the Hadamard product (or convolution) of the analytic functions f and g, and V* denote the dual set of the set V. In this paper the classes k-UCV and k-ST in terms of dual sets are descibed. Duality of mentioned classes is also used to obtain other results in the class k-UCV and k-ST. Problem of neighbourhoods of functions as well as stability of convolution in the class k-UCV and k-ST are investigated.