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Symmetry
Volume 18
Issue 1
10.3390/sym18010089
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Geometric and Functional Symmetries in q-Bernoulli Polynomial Generated Bi-Univalent Function Subfamilies

by
Sondekola Rudra Swamy
1,†,
Basem Aref Frasin
2,†,
Ibtisam Aldawish
3,*,† and
Vinutha Raghu
1,†
1
Department of Information Science and Engineering, Acharya Institute of Technology, Bengaluru 560 107, India
2
Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq 25113, Jordan
3
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Symmetry 2026, 18(1), 89; https://doi.org/10.3390/sym18010089 (registering DOI)
Submission received: 24 November 2025 / Revised: 16 December 2025 / Accepted: 29 December 2025 / Published: 4 January 2026
(This article belongs to the Special Issue Symmetry and Its Applications in Complex Analysis by the Means of Special Functions)
Versions Notes

Abstract

This study is inspired by the rich symmetry and diverse applications of special polynomial families, with a particular focus on the q-Bernoulli polynomials, which have recently emerged as significant tools in bi-univalent function theory. These polynomials are distinguished by their mathematical versatility, analytical manageability, and strong potential for generalization, offering an elegant framework for advancing the study of such functions. In this paper, we introduce a novel subclass of bi-univalent functions defined through q-Bernoulli polynomials. We obtain coefficient estimates for functions in this class and investigate their implications for the Fekete–Szegö functional. Additionally, we present several new results to enrich the theoretical landscape of bi-univalent functions associated with q-Bernoulli polynomials.
Keywords: bi-univalent functions; Fekete–Szegö functional; holomorphic functions; q-Bernoulli polynomials; subordination bi-univalent functions; Fekete–Szegö functional; holomorphic functions; q-Bernoulli polynomials; subordination

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MDPI and ACS Style

Swamy, S.R.; Frasin, B.A.; Aldawish, I.; Raghu, V. Geometric and Functional Symmetries in q-Bernoulli Polynomial Generated Bi-Univalent Function Subfamilies. Symmetry 2026, 18, 89. https://doi.org/10.3390/sym18010089

AMA Style

Swamy SR, Frasin BA, Aldawish I, Raghu V. Geometric and Functional Symmetries in q-Bernoulli Polynomial Generated Bi-Univalent Function Subfamilies. Symmetry. 2026; 18(1):89. https://doi.org/10.3390/sym18010089

Chicago/Turabian Style

Swamy, Sondekola Rudra, Basem Aref Frasin, Ibtisam Aldawish, and Vinutha Raghu. 2026. "Geometric and Functional Symmetries in q-Bernoulli Polynomial Generated Bi-Univalent Function Subfamilies" Symmetry 18, no. 1: 89. https://doi.org/10.3390/sym18010089

APA Style

Swamy, S. R., Frasin, B. A., Aldawish, I., & Raghu, V. (2026). Geometric and Functional Symmetries in q-Bernoulli Polynomial Generated Bi-Univalent Function Subfamilies. Symmetry, 18(1), 89. https://doi.org/10.3390/sym18010089

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