On Montel’s theorem and Yang’s problem

Let F be a family of meromorphic functions defined in a domain D, and let ψ (/≡ 0) be a function meromorphic in D. For every function f ∈ F, if (1) f has only multiple zeros; (2) the poles of f have multiplicity at least 3; (3) at the common poles of f and ψ, the multiplicity of f does not equal the multiplicity of ψ; (4) f(z) = ψ(z), then F is normal in D. This gives a partial answer to a problem of L. Yang, and generalizes Montel’s theorem. Some examples are given to show the sharpness of our result.  2004 Elsevier Inc. All rights reserved