Applications of $ q- $Ultraspherical polynomials to bi-univalent functions defined by $ q- $Saigo's fractional integral operators

This study established upper bounds for the second and third coefficients of analytical and bi-univalent functions belonging to a family of particular classes of analytic functions utilizing $ q- $Ultraspherical polynomials under $ q- $Saigo's fractional integral operator. We also discussed the...

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Bibliographic Details
Published inAIMS mathematics Vol. 9; no. 7; pp. 17063 - 17075
Main Authors Al-Hawary, Tariq, Amourah, Ala, Alsoboh, Abdullah, Ogilat, Osama, Harny, Irianto, Darus, Maslina
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
analytic functions
bi-univalent functions
q- $calculus
q- $ultraspherical polynomials
univalent functions
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Summary:This study established upper bounds for the second and third coefficients of analytical and bi-univalent functions belonging to a family of particular classes of analytic functions utilizing $ q- $Ultraspherical polynomials under $ q- $Saigo's fractional integral operator. We also discussed the Fekete-Szegö family function problem. As a result of the specialization of the parameters used in our main results, numerous novel outcomes were demonstrated.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2024828