Univalent functions defined by Ruscheweyh derivatives

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.

Keywords

• Hadamard product
• starlike
• univalent.