Geometric Properties of Certain Classes of Analytic Functions Associated with a q-Integral Operator

This article presents certain families of analytic functions regarding q-starlikeness and q-convexity of complex order gamma (gamma is an element of 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 (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.