Sharp initial coefficient bounds and the Fekete–Szegö problem for some certain subclasses of analytic and bi-univalent functions

Abstract

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 .