Roper-Suffridge extension operator on a reinhardt domain

Let pj∈ℕ and pj≥1,j=2,…,k,k≥2, be a fixed positive integer. We introduce a Roper-Suffridge extension operator on the following Reinhardt domain given by , where f is a normalized biholomorphic function on the unit disc D, and for 2≤j≤k,Pj:ℂnj→ℂ is a homogeneous polynomial of degree pj and . In this paper, some conditions for pj are found under which the operator preserves the properties of almost starlikeness of order α, starlikeness of order α and strongly starlikeness of order α on ΩN, respectively.