Convolution Properties of q-Janowski-Type Functions Associated with (x,y)-Symmetrical Functions

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 sup...

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Bibliographic Details
Published in:Symmetry (Basel) 2022-07, Vol.14 (7), p.1406
Main Authors: Alsarari, Fuad, Alzahrani, Samirah
Format: Article
Language:English
Subjects:
(x,y)-symmetrical functions
(ρ,q)-neighborhood
Analytic functions
Calculus
Convolution
Hadamard product
Mathematical analysis
Neighborhoods
q-calculus
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Summary: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.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14071406