Applications of q-difference symmetric operator in harmonic univalent functions

Abstract

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 Heqm (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 Heqm (α) and obtain sharp coefficient bounds, distortion theorems and covering results. Furthermore, we also highlight some known consequence of our main results.