SHARP INITIAL COEFFICIENT BOUNDS AND THE FEKETE-SZEGO PROBLEM FOR SOME SUBCLASSES OF ANALYTIC AND BI-UNIVALENT FUNCTIONS

We introduce two new subclasses U-Sigma(alpha,lambda) and B-1 Sigma(alpha) of analytic bi-univalent functions defined in an open unit disk U, which are associated with the Bazilevich functions. In addition, for functions from 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-Szego functional a(3) - mu a(2)(2).