### Some classes of analytic functions associated with q-Ruscheweyh differential operator

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#### Abstract

q-analysis (q-calculus) has many applications in mathematics and

physics. $q$-Derivative $D_q$ of a function $f$, analytic in open

unit disc, is defined as $D_qf(z)=\frac{f(qz)-f(z)}{(q-1)z},$ $q\in

(0,1),$ $(z\neq0)$ and $D_qf(0)=f'(0).$ Using $q$-analogue of well

known Ruscheweyh differential operator $D^n_q$ of order $n,$ we

introduce certain classes $ST_q(n)$ for $n=0,1,2,...,$ and

investigate a number of interesting properties such as inclusion and

coefficient results.

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