ANOTHER IMPROVEMENT OF MONTEL'S CRITERION

Let f be a family of meromorphic functions defined in a domain D subset of C, let psi(1), psi(2) and psi(3) be three meromorphic functions such that psi(i)(z) not equivalent to psi(j)(z) (i not equal j) in D, one of which may be infinity identically, and let l(1), l(2) and l(3) be positive integers or infinity with 1/l(1) + 1/l(2) + 1/l(3) < 1. Suppose that, for each f is an element of f and z is an element of D, (1) all zeros of f - psi(i) have multiplicity at least l(i) for i = 1,2,3; (2) f (z(0)) not equal psi(i)(z(0)) if there exist i, j is an element of {1,2,3} (i not equal j) and z(0) is an element of D such that psi(i)(z(0)) = psi(j)(z(0)). Then f is normal in D. This improves and generalizes Montel's criterion.