Generalized q-starlike harmonic functions

In this paper a class S-H(0) (n, q, A, B) of harmonic functions f is an element of H-0, associated with a q-Ruscheweyh operator is defined. A necessary and sufficient convolution condition for a function f is an element of H-0 to be in this class is proved. A sufficient coefficient condition for the harmonic functions to be in S-H(0) (n, q, A, B) and to be sense preserving and univalent is also obtained. It is proved that this coefficient condition is also necessary for the functions in its subclass T S-H(0) (n, q, A, B). Using this necessary and sufficient coefficient condition, results based on the convexity and compactness of the class T S-H(0) (n, q, A, B), extreme points for the functions in the class T S-H(0) (n, q, A, B) are obtained. Further results on the radii of q -starlikeness of order a, for the functions in the class T S-H(0) (n, q, A, B) are obtained.