**5. Conclusions**

In this article, we have defined a new class of multivalent *q*-starlike functions by using multivalent *q*-Ruscheweyh differential operator. We studied some interesting problems, which are helpful to study the geometry of the image domain, and also used some of the achieved results to find the growth of Hankel determinant. The idea of this determinant is applied in the theory of singularities [39] and in the study of power series with integral coefficients. For deep insight, the reader is invited to read [38–44]. Further, we have generalized the Bernardi integral operator and defined the multivalent *q*-Bernardi integral operator. Some useful properties of this class of multivalent functions have been studied.

**Author Contributions:** The authors have equally contributed to accomplish this research work.

**Funding:** This article is supported financially by the Anyang Normal University, Anyang 455002, Henan, China. **Conflicts of Interest:** The authors agree with the contents of the manuscript, and there are no conflicts of interest among the authors.
