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Research Article | Open Access

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

Tariq Al-Hawary1( ), Ala Amourah2( ), Abdullah Alsoboh3( ), Osama Ogilat4, Irianto Harny5, Maslina Darus6
Department of Applied Science, Ajloun College, Al Balqa Applied University, Ajloun 26816, Jordan
Mathematics Education Program, Faculty of Education and Arts, Sohar University, Sohar 3111, Oman
Department of Mathematics, Faculty of Science, Philadelphia University, 19392 Amman, Jordan
Department of Basic Sciences, Faculty of Arts and Science, Al-Ahliyya Amman University, Amman 19328, Jordan
Department General Education, Faculty of Resilience, Rabdan Academy, Abu Dhabi, United Arab Emirates
Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia
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Abstract

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.

Keywords

qUltraspherical polynomialsunivalent functionsbi-univalent functionsqcalculusanalytic functions
CLC number: 30C45

References

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AIMS Mathematics
Volume 9 Issue 7,
July 2024
Pages 17063-17075
DOI: 10.3934/math.2024828

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Cite this article:
Al-Hawary T, Amourah A, Alsoboh A, et al. Applications of q −Ultraspherical polynomials to bi-univalent functions defined by q −Saigo's fractional integral operators. AIMS Mathematics, 2024, 9(7): 17063-17075. https://doi.org/10.3934/math.2024828

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Received: 06 December 2023
Revised: 04 April 2024
Accepted: 10 April 2024
Published: 15 July 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)