AVOIDANCE CRITERIA FOR NORMAL FAMILIES AND NORMAL FUNCTIONS

Functions F and G are said to avoid each other if F – G is never zero, and F and G are never simultaneously infinite. Bargman, Bonk, Hinkkanen, and Martin proved that a family of functions meromorphic in the unit disk D is a normal family if there exist three functions G₁, G₂, and G₃, each continuous in D, such that for each the functions f, G₁, G₂, and G₃ all avoid each other. We present some variations and consequences of this result, and give a sufficient condition of the same type for a funcion to be a normal function. We also give some examples of functions that do not avoid normal functions.