Applications of q-difference symmetric operator in harmonic univalent functions

In this paper, for the first time, we apply symmetric q -calculus operator theory to define symmetric Salagean q-differential operator. We introduce a new class Hqᵐ(α ) of harmonic univalent functions f associated with newly defined symmetric Salagean q-differential operator for complex harmonic functions. A sufficient coefficient condition for the functions f to be sense preserving and univalent and in the same class is obtained. It is proved that this coefficient condition is necessary for the functions in its subclass Hqᵐ(α ) and obtain sharp coefficient bounds, distortion theorems and covering results. Furthermore, we also highlight some known consequence of our main results.