Applications of higher-order derivatives to subclasses of multivalent q-starlike functions

Three new subfamilies of multivalent (or p-valent) q-starlike functions with respect to higher-order q-derivatives are introduced. Several properties of such families of q-starlike functions with negative coefficients including distortion theorems and radius problems are derived. For the motivation and validity of the results which are presented here, relevant connections of our findings with those that were given in earlier work are also pointed out. Finally, we have chosen to reiterate the well-demonstrated fact that any attempt to produce the rather straightforward (p, q)-variations of the results, which we have presented in this article, will be a rather trivial and inconsequential exercise, simply because the additional parameter p is obviously redundant.