Region of variability for close-to-convex functions-II

摘要

For a complex number α with Reα>0 let Kϕ(α) be the class of analytic functions f in the unit disk D with f(0)=0 satisfying Re(f′(z)/ϕ′(z))>0 in D,f′(0)/ϕ′(0)=α, for some convex univalent function ϕ in D. For any fixed z0∈D, and λ∈D¯ we shall determine the region of variability Vϕ(z0,α,λ) for f(z0) when f ranges over the classKϕ(α,λ)=f∈Kϕ(α):ddzf′(z)ϕ′(z)z=0=2λ(Reα).In the final section we graphically illustrate the region of variability for several sets of parameters z0 and α.