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

∗ Partially supported by grant No. 433/94 NSF of the Ministry of Education and Science of the Republic of Bulgaria 1991 Mathematics Subject Classification:30C45 We consider functions of the type, j=1 ... n, F(z) = z^p ∏ [ fj (z)/(z^p) ] ^αj where fj are p-valent functions starlike of order αj and aj are complex numbers. The problem we solve is to find conditions for the centre and the radius of the disc {z : |z − ω| < r}, contained in the unit disc {z : |z| < 1} and containing...