Coefficient Bounds for a Certain Subclass of Bi-Univalent Functions Associated with Lucas-Balancing Polynomials

Abdulmtalb Hussen () and Mohamed Illafe
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Abdulmtalb Hussen: School of Engineering, Math and Technology, Navajo Technical University, Lowerpoint Rd State Hwy 371, Crownpoint, NM 87313, USA
Mohamed Illafe: School of Engineering, Math and Technology, Navajo Technical University, Lowerpoint Rd State Hwy 371, Crownpoint, NM 87313, USA

Mathematics, 2023, vol. 11, issue 24, 1-8

Abstract: In this paper, we introduce a new subclass of bi-univalent functions defined using Lucas-Balancing polynomials. For functions in each of these bi-univalent function subclasses, we derive estimates for the Taylor–Maclaurin coefficients a 2 and a 3 and address the Fekete–Szegö functional problems for functions belonging to this new subclass. We demonstrate that several new results can be derived by specializing the parameters in our main findings. The results obtained from this study will enrich the theoretical foundation of this field and open new avenues for mathematical inquiry and application.

Keywords: Balancing polynomial; Lucas-Balancing polynomials; bi-univalent functions; analytic functions; Taylor–Maclaurin coefficients; Fekete–Szegö functional (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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