A Generalization of Gegenbauer Polynomials and Bi-Univalent Functions

Three subclasses of analytic and bi-univalent functions are introduced through the use of q−Gegenbauer polynomials, which are a generalization of Gegenbauer polynomials. For functions falling within these subclasses, coefficient bounds a2 and a3 as well as Fekete–Szegö inequalities are derived. Spec...

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Bibliographic Details
Published in:Axioms 2023-01, Vol.12 (2), p.128
Main Authors: Amourah, Ala, Alsoboh, Abdullah, Ogilat, Osama, Gharib, Gharib Mousa, Saadeh, Rania, Al Soudi, Maha
Format: Article
Language:English
Subjects:
analytic functions
bi-univalent functions
Fekete–Szegö problem
Functional analysis
Functions (mathematics)
Mathematical analysis
Ordinary differential equations
Polynomials
q–calculus
q–Gegenbauer polynomials
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Summary:Three subclasses of analytic and bi-univalent functions are introduced through the use of q−Gegenbauer polynomials, which are a generalization of Gegenbauer polynomials. For functions falling within these subclasses, coefficient bounds a2 and a3 as well as Fekete–Szegö inequalities are derived. Specializing the parameters used in our main results leads to a number of new results.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms12020128