Domains of Univalence for Typically-real Odd Functions

Abstract

The univalence problems in the class of typically-real functions were considered by Golusin [G. Golusin (1950). On typically-real functions, (Russian). Mat. Sb. , 27 (69), 201-218]. He proved that the domain of local and global univalence for typically-real functions coincide. In this note we have proved that this is not the case for typically-real odd functions. Moreover, we have observed that for this class there can be infinitely many domains of univalence. We have determined some of them.