On univalent functions defined by a generalized Sǎlǎgean operator

Abstract

We introduce a class of univalent functions Rn (λ,a) defined by a new differential operator Dnf (z), nε□0= {0,1,2,...}, where D0f (z)=f (z), D1f (z)= (1-λ)f (z) +λzf' (z)=Dλf (z), λ≥0, and Dnf (z)=Dλ (D n-1f (z)). Inclusion relations, extreme points of Rn (λ,a), some convolution properties of functions belonging to Rn (λ,a), and other results are given. Copyright © 2004 Hindawi Publishing Corporation. All rights reserved.