On Typically Real Functions Which Omit Two Conjugated Values

Abstract

Abstract. In this paper we discuss the class Tp,e consisting of typically real functions which do not admit values wo = pe lB and wo-We estimate the second and the third coefficients of a function / 6 TPi$ and we determine the Koebe domain for the class of typically real functions with fixed second coefficient.Let T denote the class of analytic functions / in the unit disk A = {z G C : \z\ < 1} and normalized by /(0) = /'(0) -1 = 0 for which the condition