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International Journal of Mathematics and Mathematical Sciences
Volume 2004, Issue 27, Pages 1429-1436

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 Hindawi Publishing Corporation. 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.


We introduce a class of univalent functions Rn(λ,α) defined by a new differential operator Dnf(z), n0={0,1,2,}, where D0f(z)=f(z), D1f(z)=(1λ)f(z)+λzf(z)=Dλf(z), λ0, and Dnf(z)=Dλ(Dn1f(z)). Inclusion relations, extreme points of Rn(λ,α), some convolution properties of functions belonging to Rn(λ,α), and other results are given.