On Bieberbach-Eilenberg functions. II
James A. Jenkins · Transactions of the American Mathematical Society · 1955
are uniformly bounded. Rogosinski [9] raised the question of the best possible bound P(X) for the functions in C(X). He gave certain upper estimates for P(X) but not the precise value. The object of the present paper is to give the complete solution of this problem by a method used earlier to solve certain other questions for the same class of functions [5 1. 2. We begin by solving first the related problem of the closest boundary point to the origin of the image of I zj <1 by a univalent function in C(X). In the ?-plane ( =t+iqi) we regard the domain Az(t) defined by