SUPPORT-POINTS AND DOUBLE POLES

This paper gives some sufficient conditions for support points of the class S of univalent functions to be rotations of the Koebe function k (z) = z(1 - z)(-2). If f is a support point associated with a continuo us linear functional L and if the function Phi(w) = L(f(2)/(f - w)) do es not have a double pole, then under some mild additional assumptions , a rational support point f must be a rotation of the Koebe function. The situation is more complicated when Phi has a double pole. However , we are able to prove the two-functional conjecture for derivative fu nctionals, where Phi has a double pole.