A generalized operator involving the $q$-hypergeometric function

Aabed Mohammed, Maslina Darus

Motivated by the familiar $q$-hypergeometric functions, we introduce here a new general operator. By this operator, we define a subclass of analytic function. The class generalizes well known classes of starlike and convex functions. The integral means inequalities of this class are investigated. Also, we consider $p$-$\gamma$-neighborhood for functions in this class. Our result contains some interesting corollaries as its special cases.