Koebe sets for the class of functions convex in two directions.

In this paper, we consider a class Kαof all functions f univalent in the unit disk Δ that are normalized by f(0) = f' (0) - 1 = 0 while the sets f(Δ) are convex in two symmetric directions: eiαπ/2 and e -iαπ/2, α ∈ [0, 1] . It means that the intersection of f(Δ) with each straight line having the direction eiαπ/2 or e-iαπ/2 is either a compact set or an empty set. We find the Koebe set for Kα. Moreover, we perform the same operation for functions in Kβ,γ, i.e. for functions that are convex in two fixed directions: eiβπ/2 and eiγπ/2, -1 ≤ β ≤ γ γ ≤ 1. [ABSTRACT FROM AUTHOR]