Taylor-Maclaurin coefficients and the Fekete-Szegö inequalities for certain subclasses of bi-univalent functions involving the Gegenbauer polynomials

Volume 33, Issue 2, pp 155--168 https://dx.doi.org/10.22436/jmcs.033.02.04

Publication Date: December 19, 2023 Submission Date: August 16, 2023 Revision Date: September 19, 2023 Accteptance Date: November 16, 2023

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Authors

M. Younis - School of Mathematical Sciences and Shanghai Key Laboratory of PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, Peoples Republic of China. B. Khan - School of Mathematical Sciences and Shanghai Key Laboratory of PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, Peoples Republic of China. Z. Salleh - Department of Mathematics, Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, 21030 Kuala, Nerus, Terengganu, Malaysia. M. Ibrahim - College of Engineering, University of Buraimi, Al Buraimi, Sultanate of Oman. F. M. O. Tawfiq - Mathematics Department, College of Science, King Saud University, P.O. Box 22452 Riyadh 11495, Saudi Arabia. F. Tchier - Mathematics Department, College of Science, King Saud University, P.O. Box 22452 Riyadh 11495, Saudi Arabia. T. G. Shaba - Department of Mathematics, Landmark University, Omu-Aran 251103, Nigeria.

Abstract

In this paper by using the idea of Gegenbauer polynomials, we introduced certain new subclasses of analytic and bi-univalent functions. Additionally, we determined the estimates for first two Taylor-Maclaurin coefficients and the Fekete-Szegö functional problems for each of the function classes we defined. In the concluding part, we recall the curious readers attention to the possibility of analyzing the result's \(q\)-generalizations presented in this article. Moreover, according to the proposed extension, the \((\mathfrak{ p},q)\)-extension will only be comparatively small and inconsequently change, as the additional parameter \(\mathfrak{p}\) is redundant.

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Keywords

• Analytic function
• bi-univalent function
• Gegenbauer polynomials
• coefficient estimates
• subordination
• Fekete-Szegö functional problems

MSC

•  30C45
•  30D30

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