UNIFIED SOLUTION OF FEKETE-SZEGO PROBLEM FOR SUBCLASSES OF STARLIKE MAPPINGS IN SEVERAL COMPLEX VARIABLES

Let S-phi* be a subclass of starlike functions in the unit disk U; where phi is a convex function such that phi(0) = 1, phi'(0) > 0, R(phi(xi)) > 0 and phi(U) is symmetric with respect to the real axis. We obtain the sharp solution of Fekete-Szego problem for the family S-phi*, and then extend the result to the case of corresponding subclass defined on the bounded starlike circular domain Omega in several complex variables, which give an unified answer of Fekete-Szego problem for the kinds of subclasses of starlike mappings de fined on Omega. At last, we propose two conjectures related the same problems on the unit ball in a complex Banach space and on the unit polydisk in C-n. (C) 2019 Mathematical Institute Slovak Academy of Sciences