Geometric properties of certain classes of analytic functions associated with a \(q\)-integral operator (Q2338066)

Summary: This article presents certain families of analytic functions regarding \(q\)-starlikeness and \(q\)-convexity of complex order \(\gamma(\gamma \in \mathbb{C} \backslash \left\{0\right\})\). This introduced a \(q\)-integral operator and certain subclasses of the newly introduced classes are defined by using this \(q\)-integral operator. Coefficient bounds for these subclasses are obtained. Furthermore, the \((\delta,q)\)-neighborhood of analytic functions are introduced and the inclusion relations between the \((\delta,q)\)-neighborhood and these subclasses of analytic functions are established. Moreover, the generalized hyper-Bessel function is defined, and application of main results are discussed.