View article

Let F₁ (F₂ respectively) denote the class of analytic functions f in the unit disk |z|<1 with f(0)=0=f^′(0)−1 satisfying the condition ReP_f(z)<3/2 (ReP_f(z)>−1/2 respectively) in |z|<1, where P_f(z)=1+zf^″(z)/f^′(z). For any fixed z₀ in the unit disk and λ∈[0,1), we shall determine the region of variability for logf^′(z₀) when f ranges over the class {f∈F₁:f^″(0)=−λ} and {f∈F₂:f^″(0)=3λ}, respectively.