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

S. L. Shukla and Vinod Kumar

 Department of Mathematics, Janta College, Bakewar, Etawah 206124, India
Received 28 September 1982; Revised 8 August 1983

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.