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In this paper, we introduced two novel subclasses of bi-univalent functions, M_ (, B (x, ) ) and H_ (, , B (x, ) ), utilizing Lucas-Balancing polynomials. Within these function classes, we established bounds for the Taylor-Maclaurin coefficients |a₂| and |a₃|, addressing the Fekete-Szegö functional problems specific to functions within these new subclasses. Moreover, we illustrated how our primary findings could lead to various new outcomes through parameter specialization.
Hussen et al. (Mon,) studied this question.