International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 3, Pages 483-486
doi:10.1155/S0161171283000435
Univalent functions defined by Ruscheweyh derivatives
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.
Abstract
We study some radii problems concerning the integral operator
F(z)=γ+1zγ∫°zuγ−1f(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.