Criteria for starlikeness for holomorphic mappings

Abstract

Let Ω ⊂ ℂⁿ be a domain, z = (z₁,…,z_n) ∈ Ω, f (z) = (f ₁(z), …, f _n(z)) be holomorphic mapping, and let w ₀ ∈ f (Ω). Then f (Ω) is called starlike with respect to w ₀ if for any point w ∈ f (Ω), the line segment joining w ₀ and w lies in f (Ω). A convex mapping is a starlike mapping. Actually, we may define a convex mapping as a mapping that is starlike with respect to any interior point of f (Ω). In this book, we usually assume that f (0) = 0 and that f is a starlike mapping with respect to the origin.