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Complex-valued harmonic functions that are univalent and sense preserving in the open unit disk can be written in the form $f=h+\overline{g}$, where h and g are analytic. In this paper we investigate some classes of univalent harmonic functions with varying coefficients related to Janowski functions. By using the extreme points theory we obtain necessary and sufficient convolution conditions, coefficients estimates, distortion theorems, and integral mean inequalities for these classes of functions. The radii of starlikeness and convexity for these classes are also determined. [ABSTRACT FROM AUTHOR]

In the present paper we define a class of products of multivalent close-to-star functions and determine the set of pairs [InlineEquation not available: see fulltext.], [InlineEquation not available: see fulltext.], such that every function from the class maps the disk [InlineEquation not available: see fulltext.] onto a domain starlike with respect to the origin. Some consequences of the obtained result are also considered. MSC: 30C45, 30C50, 30C55. [ABSTRACT FROM AUTHOR]

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 [InlineEquation not available: see fulltext.] 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. MSC: 30C45, 30C50, 30C55. [ABSTRACT FROM AUTHOR]