Geometric properties of certain classes of analytic functions associated with a q-integral operator

Abstract

This article presents certain families of analytic functions regarding q-starlikeness and q-convexity of complex order γ (γ ∈ C\ 0). 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 (δ, q)-neighborhood of analytic functions are introduced and the inclusion relations between the (δ, 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.