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We introduce a new subclass of functions defined by multiplier differential operator and give coefficient bounds for these subclasses. Also, we obtain necessary and sufficient convolution conditions, distortion bounds and extreme points for these subclasses of functions. [ABSTRACT FROM AUTHOR]

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 this paper we investigate some generalizations of classes of harmonic functions. By using the extreme points theory we obtain coefficients estimates distortion theorems and integral mean inequalities in these classes of functions. [ABSTRACT FROM AUTHOR]

New classes of univalent harmonic functions are introduced. We give sufficient coefficient conditions for these classes. These coefficient conditions are shown to be also necessary if certain restrictions are imposed on the coefficients of these harmonic functions. By using extreme points theory we also obtain coefficients estimates, distortion theorems, and integral mean inequalities for these classes of functions. Radii of convexity and starlikeness of the classes are also considered. [ABSTRACT FROM AUTHOR]

In the paper we define classes of harmonic starlike functions with respect to symmetric points and obtain some analytic conditions for these classes of functions. Some results connected to subordination properties, coefficient estimates, integral representation, and distortion theorems are also obtained. [ABSTRACT FROM AUTHOR]