On products of starlike functions. I

We deal with functions given by the formula ${\displaystyle F\left(z\right)=zG\prime \left(z\right)=z{\prod }_{j=1}^n{\left(\frac{f_j\left(z\right)}{z}\right)}^{a_j}}$ where ${\displaystyle f_j\left(z\right)}$ are starlike of order ${\displaystyle {\alpha }_j}$ and ${\displaystyle a_j}$ are complex constants. In particular, radii of starlikeness and convexity as well as orders of starlikeness and convexity are found.