We derive theq-analogue of the well-known Ruscheweyh differential operator using the concept ofq-derivative. Here, we investigate several interesting properties of thisq-operator by making use of the method of differential subordination.

We study a class of complex-valued harmonic univalent functions using a generalized operator involving basic hypergeometric function. Precisely, we give a necessary and sufficient coefficient condition for functions in this class. Distortion bounds, extreme points, and neighborhood of such functions are also considered.

By making use of basic hypergeometric functions, a class of complex harmonic meromorphic functions with positive coefficients is introduced. We obtain some properties such as coefficient inequality, growth theorems, and extreme points.

We derive the Fekete-Szegö theorem for new subclasses of analytic functions which areq-analogue of well-known classes introduced before.

In this paper, we consider a new subclass of analytic and bi-univalent functions associated with q-Ruscheweyh differential operator in the open unit disk U. For functions belonging to the class Σ q (λ, φ), we obtain estimates on the first two Taylor-Maclaurin coefficients. Further, we derive another subclass of analytic and bi-univalent functions as a special consequences of the results.