International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 9, Pages 567-575
doi:10.1155/S0161171202007202
On the univalency for certain subclass of analytic
functions involving Ruscheweyh derivatives
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.
Abstract
Let H
be the class of functions f(z) of the form f(z)=z+∑ K=2 + ∞a k z k, 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.