ON SUBCLASSES OF ANALYTIC FUNCTIONS INVOLVING $q$-DERIVATIVE OPERATOR WITH NEGATIVE COEFFICIENTS

The purpose of this work is to introduce and study new subclasses of analytic functions using a new $q$-derivative operator. This operator generalizes the operators introduced by Al-Oboudi, Catas, Cho and Kim, Cho and Srivastava, Maslina Darus and R W Ibrahim, S$\check{a}$l$\check{a}$gean, Uralegaddi and Somanatha. We investigate coefficient bounds, growth, distortion and closure theorems for the functions belonging to these classes. We also give a result which unifies radii of close-to-convexity, starlikeness and convexity.