Inclusive Subclasses of Bi-Univalent Functions Defined by Error Functions Subordinate to Horadam Polynomials

Al-Hawary, Tariq; Frasin, Basem; Breaz, Daniel; Cotîrlă, Luminita-Ioana

doi:10.3390/sym17020211

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Inclusive Subclasses of Bi-Univalent Functions Defined by Error Functions Subordinate to Horadam Polynomials

¹

Department of Applied Science, Ajloun College, Al Balqa Applied University, Ajloun 26816, Jordan

²

Faculty of Science, Department of Mathematics, Al-Bayt University, Mafraq 25113, Jordan

³

Department of Mathematics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania

⁴

Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania

^*

Authors to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Symmetry 2025, 17(2), 211; https://doi.org/10.3390/sym17020211

Submission received: 28 December 2024 / Revised: 27 January 2025 / Accepted: 29 January 2025 / Published: 30 January 2025

(This article belongs to the Special Issue Geometric Function Theory and Special Functions II)

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Abstract

In this paper, by utilizing error functions subordinate to Horadam polynomials, we introduce the inclusive subclasses

A (a, ς, r, u, η, ρ, σ),

B (a, ς, r, u, τ, θ)

and

C (a, ς, r, u, τ, θ)

of bi-univalent functions in the symmetric unit disk U. For functions in these subclasses, we derive estimations for the Maclaurin coefficients

| k_{2} |

and

| k_{3} |,

as well as the Fekete–Szegö functional. Additionally, some related results are also obtained.

Keywords: analytic; univalent; bi-univalent functions; error functions; Horadam polynomials; Fekete–Szegö

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MDPI and ACS Style

Al-Hawary, T.; Frasin, B.; Breaz, D.; Cotîrlă, L.-I. Inclusive Subclasses of Bi-Univalent Functions Defined by Error Functions Subordinate to Horadam Polynomials. Symmetry 2025, 17, 211. https://doi.org/10.3390/sym17020211

AMA Style

Al-Hawary T, Frasin B, Breaz D, Cotîrlă L-I. Inclusive Subclasses of Bi-Univalent Functions Defined by Error Functions Subordinate to Horadam Polynomials. Symmetry. 2025; 17(2):211. https://doi.org/10.3390/sym17020211

Chicago/Turabian Style

Al-Hawary, Tariq, Basem Frasin, Daniel Breaz, and Luminita-Ioana Cotîrlă. 2025. "Inclusive Subclasses of Bi-Univalent Functions Defined by Error Functions Subordinate to Horadam Polynomials" Symmetry 17, no. 2: 211. https://doi.org/10.3390/sym17020211

APA Style

Al-Hawary, T., Frasin, B., Breaz, D., & Cotîrlă, L.-I. (2025). Inclusive Subclasses of Bi-Univalent Functions Defined by Error Functions Subordinate to Horadam Polynomials. Symmetry, 17(2), 211. https://doi.org/10.3390/sym17020211

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Inclusive Subclasses of Bi-Univalent Functions Defined by Error Functions Subordinate to Horadam Polynomials

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