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 517.5We introduce two new subclasses $\mathcal{U}_{Σ}(α,λ)$ and ${\mathcal{B}_1}_{Σ}(α)$ of analytic bi-univalent functions defined in the open unit disk $\mathbb{U}$, 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 $a_3-μ a_2^2.$