On Generalizations of the Close-to-Convex Functions Associated with q -Srivastava–Attiya Operator

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 K q , b s h , K ˜ q , s b h , Q q , b s h , and Q ˜ q , s b h 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.