Inequalities for the Angular Derivative of an Analytic Function in the Unit Disk

Let $ be a function, analytic in the unit disk, D, that maps the unit disk into itself ((z) ^ 2). In this paper, we present some inequalities for the angular derivative of cj). The more important of these concern the derivative of $ at its fixed points in the closed unit disk. Since (f) and 0' need not be continuous in D we need to clarify the terms "fixed point" and "derivative of ^ at a fixed point".