Samira Rahrovi

Let f be a locally univalent function on the unit disk U. We consider the normalized extensions of f to the Euclidean unit ball B n ⊆ C n given by Φn,γ(f)(z) = ( f(z1), ( f ′ (z1) )γ zˆ ) , where γ ∈ [0, 1/2], z = (z1, zˆ) ∈ B n and Ψn,β(f)(z) = ( f(z1), ( f(z1) z1 )β zˆ ) , in which β ∈ [0, 1], f(z1) ̸= 0 and z = (z1, zˆ) ∈ B n . In the case γ = 1/2, the function Φn,γ(f) reduces to the well known Roper-Suffridge extension operator. By using different methods, we prove that if f is parabolic starlike mapping on U then Φn,γ(f) and Ψn,β(f) are parabolic starlike mappings on B