The paper concerns complex-valued functions which are holomorphic in bounded complete n-circular domains and fulfil some geometric conditions. The families of such kind of functions were considered for instance by Bavrin [1,2], Dobrowolska and Liczberski [4], Dziubiński and Sitarski [5], Fukui [6], Higuchi [8], Jakubowski and Kamiński [9], Liczberski and Wrzesień [14], Marchlewska [15,16], Michiwaki [17], and Stankiewicz [22]. The above functions were applied later to research some families of locally biholomorphic mappings in (see for instance Pfaltzgraff and Suffridge [19], Liczberski [12], Hamada, Honda and Kohr [7]). In this paper, we consider an interesting family of the type which separates two Bavrin’s families . These families correspond to the well-known families of convex univalent and close-to-convex univalent functions of one variable, respectively. We define using the property of evenness of functions. We obtain for some embedding theorems relevant to the mentioned separation question. Applying the Minkowski function of , we solve also some extremal problems for functions from . As an application, we give a topologic property of the family .