Some General Classes of q-Starlike Functions Associated with the Janowski Functions

By making use of the concept of basic (or q-) calculus, various families of q-extensions of starlike functions of order α in the open unit disk U were introduced and studied from many different viewpoints and perspectives. In this paper, we first investigate the relationship between various known classes of q-starlike functions that are associated with the Janowski functions. We then introduce and study a new subclass of q-starlike functions that involves the Janowski functions. We also derive several properties of such families of q-starlike functions with negative coefficients including (for example) distortion theorems.