Applications of q-Symmetric Derivative Operator to the Subclass of Analytic and Bi-Univalent Functions Involving the Faber Polynomial Coefficients

In this paper, using the basic concepts of symmetric q-calculus operator theory, we define a symmetric q-difference operator for m-fold symmetric functions. By considering this operator, we define a new subclass ℛbφ,m,q of m-fold symmetric bi-univalent functions in open unit disk U. As in applicatio...

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Bibliographic Details
Published in:Mathematical problems in engineering 2022-07, Vol.2022, p.1-9
Main Authors: Khan, Mohammad Faisal, Khan, Shahid, Khan, Nazar, Younis, Jihad, Khan, Bilal
Format: Article
Language:English
Subjects:
Calculus
Convex analysis
Finite differences
Functions (mathematics)
Investigations
Mathematical analysis
Operators (mathematics)
Polynomials
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Summary:In this paper, using the basic concepts of symmetric q-calculus operator theory, we define a symmetric q-difference operator for m-fold symmetric functions. By considering this operator, we define a new subclass ℛbφ,m,q of m-fold symmetric bi-univalent functions in open unit disk U. As in applications of Faber polynomial expansions for fm∈ℛbφ,m,q, we find general coefficient amk+1 for n≥4, Fekete–Szegő problems, and initial coefficients am+1 and a2m+1. Also, we construct q-Bernardi integral operator for m-fold symmetric functions, and with the help of this newly defined operator, we discuss some applications of our main results. For validity of our result, we have chosen to give some known special cases of our main results in the form of corollaries and remarks.
ISSN:1024-123X
1563-5147
DOI:10.1155/2022/4250878