Two new criteria for normal families

2005-09-22T16:52:03Z (GMT) by E.F. Clifford
A family F of meromorphic (analytic) functions is a normal family, if every infinite sequence in F has a subsequence which converges, locally uniformly on compact sub-regions, either to a meromorphic (analytic) limit or identically to infinity. Normal families have a central role in complex function theory, and are used in connection with extremal problems, harmonic functions, discontinuous groups and complex dynamical systems. In this paper, we prove two new criteria for normal families, which extend previous results by Bergweiler and Langley.