A covering theorem for odd typically-real functions

Abstract

An analytic function f(z)=z+a2z2+… in |z|<1 is typically-real if Imf(z)Imz≥0. The largest domain G in which each odd typically-real function is univalent (one-to-one) and the domain ⋂f(G) for all odd typically real functions f are obtained.

Keywords

• typically-real functions
• domain of univalence
• covering threorems.