International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 3, Pages 483-486

Univalent functions defined by Ruscheweyh derivatives

S. L. Shukla and Vinod Kumar

Department of Mathematics, Janta College, Bakewar, Etawah 206124, India

Received 28 September 1982; Revised 8 August 1983

Copyright © 1983 S. L. Shukla and Vinod Kumar. 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 study some radii problems concerning the integral operator F(z)=γ+1zγ°zuγ1f(u)du for certain classes, namely Kn and Mn(α), of univalent functions defined by Ruscheweyh derivatives. Infact, we obtain the converse of Ruscheweyh's result and improve a result of Goel and Sohi for complex γ by a different technique. The results are sharp.