The aim in the present work is to introduce and study new subclasses of analytic functions that are defined by using the generalized classes of Janowski functions combined with the (n, m)-symmetrical functions, that generalize many others defined by different authors. We gave a representation theorem for these classes, certain inherently properties, while covering and distortion properties are also pointed out.

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In this note, the concept of N -symmetric points. Janowski functions and the conic regions are combined to define a class of functions in a new interesting domain which represents the conic type regions. certain interesting coefficient inequalities are deduced.

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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˜qx,y(α,β) and K˜qx,y(α,β), and then investigate the related neighborhood results, which are also pointed out.