Region of variability for functions with positive real part

For γ∈ℂ such that {pipe}γ{pipe}<π/2 and 0≤β<1, let Pγ,β denote the class of all analytic functions P in the unit disk D with P(0)=1 and Re(eiγP(z))>βcosγ in D. For any fixed z0∈D and λ∈D, we shall determine the region of variability VP(z0,λ) for when P ranges over the class P(λ)={P∈Pγ,β:P′(0)=2(1-β)λe-iγcosγ}. As a consequence, we present the region of variability for some subclasses of univalent functions. We also graphically illustrate the region of variability for several sets of parameters. ©Instytut Matematyczny PAN, 2010.