On univalent functions defined by a generalized Sălăgean operator

Abstract

We introduce a class of univalent functionsRn(λ,α)defined by a new differential operatorDnf(z),n∈ℕ0={0,1,2,…}, whereD0f(z)=f(z),D1f(z)=(1−λ)f(z)+λzf′(z)=Dλf(z),λ≥0, andDnf(z)=Dλ(Dn−1f(z)). Inclusion relations, extreme points ofRn(λ,α), some convolution properties of functions belonging toRn(λ,α), and other results are given.