|
Organizers |
Avoidance criteria for normal families
by
Peter Lappan
Michigan State University
Let D denote the unit disk in the complex plane. We say that two functions f and g avoid each other if f(z) = g(z) has no solution for z in D. It is a classical result that a family F of functions meromorphic in D is a normal family if each function f in F omits the same three complex values. D. Bargman, M. Bonk, A. Hinkkanen, and G. J. Martin have proved that if F is a family of functions meromorphic in D, and if h1, h2, and h3 are three functions continuous in D such that the functions h1, h2 and h3 all avoid each other and also each f in F, then F is a normal family. In the present work, several extensions of this result are presented, along with a simplified proof. In addition, a corresponding criterion for a function f meromorphic in D to be a normal function is given. Some examples involving these criteria are given.
Date received: May 25, 2001
Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahs-04.