Classes of functions associated with bounded Mocanu variation

In the paper we introduce the class of linear combinations of functions which are subordinated to a convex function. Some relationships between this class and the class of real-valued functions with bounded variation on [0, 2 pi] are obtained. Next, we define classes of functions associated with bounded Mocanu variation. By using the properties of multivalent prestarlike functions, we obtain various inclusion relationships between defined classes of functions. Some applications of the main results are also considered.