Abstract

For analytic function $f(z)=z+a_2z^2+\cdots$ in the open unit disc $\mathbb{D}$, a new fractional operator $\mbox{D}^\lambda f(z)$ is defined. Applying this fractional operator $\mbox{D}^\lambda f(z)$ and the principle of subordination, we give new proofs for some classical results concerning the class $\cal{S}_\lambda^*(A,B,\alpha)$ of functions $f(z)$.

Keywords: Starlike, fractional integral, fractional derivative, distortion theorem.

MSC: 30C45

Pages:  165$-$171     

Volume  60 ,  Issue  3 ,  2008