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The paper presents two novel subclasses of the function class Σ, which consists of bi-univalent functions defined in the open unit disk D={ζ:|ζ|<1}. The authors investigate the properties of these new subclasses and provide estimates for the absolute values of the second, third, and fourth Taylor-Maclaurin coefficients r2, r3, and r4 for functions in these subclasses.