International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 9, Pages 567-575

On the univalency for certain subclass of analytic functions involving Ruscheweyh derivatives

Liu Mingsheng

Department of Mathematics, South China Normal University, Guangzhou 510631, China

Received 20 March 2001

Copyright © 2002 Liu Mingsheng. 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.


Let H be the class of functions f(z) of the form f(z)=z+K=2+akzk, which are analytic in the unit disk U={z;|z|<1}. In this paper, we introduce a new subclass Bλ(μ,α,ρ) of H and study its inclusion relations, the condition of univalency, and covering theorem. The results obtained include the related results of some authors as their special case. We also get some new results.