International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 27, Pages 1429-1436
doi:10.1155/S0161171204108090
On univalent functions defined by a generalized Sălăgean operator
Mathematics Department, Science Sections, Girls College of Education, Sitteen Street, Malaz, Riyadh 11417, Saudi Arabia
Received 17 August 2001; Revised 18 March 2002
Copyright © 2004 F. M. Al-Oboudi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.