Certain subclasses of bi-univalent functions using generating functions of (s, t)-Lucas and balancing Lucas polynomials

Thangamani, Stalin; Devadoss, Jeno Francis

doi:10.47974/JIM-2668

Open Access Research Article

Certain subclasses of bi-univalent functions using generating functions of (s, t)-Lucas and balancing Lucas polynomials

^*Stalin ThangamaniCorresponding authordrstalint@veltech.edu.inDepartment of MathematicsAvadiVel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and TechnologyChennai, Tamil Nadu, 600062, India0000-0002-8735-3567View full profile → , Jeno Francis Devadossjenofrancis29@gmail.comAffiliation 1Department of MathematicsAvadiVel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and TechnologyChennai, Tamil Nadu, 600062, IndiaAffiliation 2Department of MathematicsPrathyusha Engineering CollegeTiruvallur, Tamil Nadu, 602025, India0009-0007-4580-8387View full profile →

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pp. 2079–2087Vol. 29Issue 6June 2026DOI: 10.47974/JIM-2668XML

Received:: 01 Sep 2025
Published Online:: 30 Jun 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2668
Pages:: 2079–2087

Abstract

This research article investigates two subclasses of bi-univalent functions associated with (s, t)-Lucas polynomials in 𝔻. It intriguing since they are fundamental to geometric function theory. To understand the geometrical properties of these subclasses, the estimates of two initial Taylor-Maclaurin coefficients |a2| as well as |a3| are very essential. These play a vital role to explore a number of significant geometric features of subclasses. These initial coefficients provide significant information about the behavior of the function near the origin, revealing its functional characteristics, interaction with the boundary of the unit disk, and possible subclassifications. In particular, their distortion, growth behaviour, and mapping qualities. Additionally, we employ the Fekete-Szegö approximation, a technique frequently employed to derive precise constraints for these two subclasses, which traditionally gives upper bounds for |a3 – τa22|.

Keywords

Subordination Bi-univalent functions Lucas polynomials Fekete-Szegö inequality Coefficient estimates

Subject Classifications

30C4530C50

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