On univalent functions defined by a generalized Sălăgean operator

Abstract

We introduce a class of univalent functions Rn(λ,α) defined by a new differential operator Dnf(z), n∈ℕ0={0,1,2,…}, where D0f(z)=f(z), D1f(z)=(1−λ)f(z)+λzf′(z)=Dλf(z), λ≥0, and Dnf(z)=Dλ(Dn−1f(z)). Inclusion relations, extreme points of Rn(λ,α), some convolution properties of functions belonging to Rn(λ,α), and other results are given.