Sharp initial coefficient bounds and the Fekete–Szegö problem for some certain subclasses of analytic and bi-univalent functions - Patil, A. B.; Shaba, T. G. (Ukrains’kyi Matematychnyi Zhurnal, 2023)
UDC 517.5 We introduce two new subclasses U_Σ(α,λ) and B_1_Σ(α) of analytic bi-univalent functions defined in the open unit disk U, which are associated with the Bazilevich functions. In addition, for functions that belong to these subclasses, we obtain sharp bounds for the initial Taylor–Maclaurin coefficients a_2 and a_3, as well as the sharp estimate for the Fekete–Szegö functional a_3-μ a_2^2.