Some properties of fractional integrals and derivatives of univalent functions (Q1061889)

The authors study properties of \[ D_ z^{\alpha}f(z)=(1/\Gamma (1- \alpha))(d/dz)\int^{z}_{0}(f(t)/(z-t)^{\alpha})dt,\quad \alpha \in (0,1) \] and \[ D_ z^{-\alpha}f(z)=(1/\Gamma (\alpha))\int^{z}_{0}(f(t)/(z-t)^{\alpha})dt,\quad \alpha >0 \] if f belongs to certain subclasses of the class of functions starlike resp. convex in the unit disc.