LAUSR

The study of the q-analogue of the classical results of geometric function theory is currently of great interest to scholars. In this article, we define generalized classes of close-to-convex functions and quasi-convex functions with the help of the q-difference operator. Moreover, by using the q-analogues of a certain family of linear operators, the classes Kq,bsh, K˜q,sbh, Qq,bsh, and Q˜q,sbh are introduced. Several interesting inclusion relationships between these newly defined classes are discussed, and the invariance of these classes under the q-Bernadi integral operator was examined. Furthermore, some special cases and useful consequences of these investigations were taken into consideration.