Generalized Problem of Sratlikeness for Products of P-Valent Starlike Functions

∗ 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 the origin, so that its transformation by the function F be a domain starlike with respect to the origin.