Introduction

Abstract

The aim of the present book is a unified representation of some recent results in geometric function theory together with a consideration of their historical sources. These results are concerned with functions f, holomorphic or meromorphic in a domain Ω in the extended complex plane ℂ̄. The only additional condition we impose on these functions is the condition that the range f(Ω) is contained in a given domain Π ⊂ ℂ̄. This fact will be denoted by f ∈ A (Ω Π). We shall describe how one may get estimates for the derivatives f(n)(z0) , n ∈ ℕ, f ∈ A(Ω, Π) dependent on the position of z0 in Ω and f(z0) in Π. © 2009 Birkhäuser Verlag AG.