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2024 | OriginalPaper | Chapter

Exploration of New Classes of Bi-univalent Functions Defined by the Subordination Principle Using \(q\)-Gegenbauer Polynomials

Authors : Abdullah Alsoboh, Ala Amourah, Maryam Salem Alatawi, Gharib Gharib, Fethiye Sakar

Published in: Mathematical Analysis and Numerical Methods

Publisher: Springer Nature Singapore

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Abstract

In this study, we introduce a new class of bi-univalent functions constructed using \(q\)-Gegenbauer polynomials. We analyze and characterize this newly defined class of functions, and derive estimates for the Taylor-Maclaurin coefficients \(|a_{2}|\) and \(|a_{3}|\). Additionally, we investigate the formulation of functional problems specific to functions within this subclass, namely \(\left| a_{3}-\sigma a_{2}^{2}\right| \) (commonly known as the Fekete-Szegö problem). By systematically exploring parameter specialization, we discover a range of novel outcomes that shed light on various aspects of our main results, contributing to a broader understanding of the mathematical landscape under investigation.

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Title: Exploration of New Classes of Bi-univalent Functions Defined by the Subordination Principle Using -Gegenbauer Polynomials
Authors: Abdullah Alsoboh
Ala Amourah
Maryam Salem Alatawi
Gharib Gharib
Fethiye Sakar
Publisher: Springer Nature Singapore
Book: Mathematical Analysis and Numerical Methods
Print ISBN: 978-981-9748-75-4

Electronic ISBN: 978-981-9748-76-1

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-981-97-4876-1_24

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