Covering problems for functions n-fold symmetric and convex in the direction of the real axis

摘要

Let F denote the class of all functions univalent in the unit disk and convex in the direction of the real axis. In the paper we discuss the functions of the class F which are n-fold symmetric, where n is positive even integer. For the class of such functions we find the Koebe set as well as the covering set, i.e. ⋂f∈Ff(Δ) and ⋃f∈Ff(Δ). Moreover, the Koebe constant and the covering constant are obtained.