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Mathematics
Volume 14
Issue 10
10.3390/math14101712
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Article

Initial Coefficient Behavior of Bi-Univalent Functions Defined Through Bernoulli Polynomial Subordination

by
Mohamed Illafe
1,2,*,
Abdulmtalb Hussen
1,3 and
Feras Yousef
4,5
1
School of Engineering, Math & Technology, Navajo Technical University, Crownpoint, NM 87313, USA
2
Department of Mathematics, University of Benghazi, Benghazi 16063, Libya
3
Mathematics Department, College of Education, Al Zintan University, Dirj 00218, Libya
4
Department of Mathematics, The University of Jordan, Amman 11942, Jordan
5
Department of Mathematics, Hampton University, Hampton, VA 23669, USA
*
Author to whom correspondence should be addressed.
Mathematics 2026, 14(10), 1712; https://doi.org/10.3390/math14101712 (registering DOI)
Submission received: 24 March 2026 / Revised: 5 May 2026 / Accepted: 14 May 2026 / Published: 16 May 2026
(This article belongs to the Special Issue New Trends in Polynomials and Mathematical Analysis)
Versions Notes

Abstract

The study of coefficient problems for bi-univalent functions continues to play a central role in geometric function theory due to its analytical depth and wide range of applications. In this paper, we introduce a new subclass of bi-univalent functions defined through subordination to the generating function of Bernoulli polynomials. We derive explicit upper bounds for the initial Taylor–Maclaurin coefficients and establish a corresponding Fekete–Szegö-type inequality for functions in this class. The results obtained provide refined estimates that extend several known findings in the literature and reveal the effectiveness of Bernoulli polynomial subordination as a unifying framework for investigating coefficient problems in the theory of bi-univalent functions. Various special cases are also discussed to demonstrate the scope and applicability of the main results.
Keywords: analytic function; bi-univalent function; Fekete–Szegö inequality; Bernoulli polynomial analytic function; bi-univalent function; Fekete–Szegö inequality; Bernoulli polynomial

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MDPI and ACS Style

Illafe, M.; Hussen, A.; Yousef, F. Initial Coefficient Behavior of Bi-Univalent Functions Defined Through Bernoulli Polynomial Subordination. Mathematics 2026, 14, 1712. https://doi.org/10.3390/math14101712

AMA Style

Illafe M, Hussen A, Yousef F. Initial Coefficient Behavior of Bi-Univalent Functions Defined Through Bernoulli Polynomial Subordination. Mathematics. 2026; 14(10):1712. https://doi.org/10.3390/math14101712

Chicago/Turabian Style

Illafe, Mohamed, Abdulmtalb Hussen, and Feras Yousef. 2026. "Initial Coefficient Behavior of Bi-Univalent Functions Defined Through Bernoulli Polynomial Subordination" Mathematics 14, no. 10: 1712. https://doi.org/10.3390/math14101712

APA Style

Illafe, M., Hussen, A., & Yousef, F. (2026). Initial Coefficient Behavior of Bi-Univalent Functions Defined Through Bernoulli Polynomial Subordination. Mathematics, 14(10), 1712. https://doi.org/10.3390/math14101712

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