Abstract
The purpose of this paper is to define new classes of analytic functions by amalgamating the concepts of q-calculus, Janowski type functions and (x,y)-symmetrical functions. We use the technique of convolution and quantum calculus to investigate the convolution conditions which will be used as a supporting result for further investigation in our work, we deduce the sufficient conditions, Po ' lya-Schoenberg theorem and the application. Finally motivated by definition of the neighborhood, we give analogous definition of neighborhood for the classes (S) over tilde (x,y)(q)(alpha,beta) and (K) over tilde (x,y)(q) (alpha, beta), and then investigate the related neighborhood results, which are also pointed out.