On Miranda's Normal Criterion

摘要

In this paper, we study the normality of a family of analytic functions and prove the following theorem. Let F be a family of analytic functions in a domain D, k be a positive integer and a(z), a_1(z), a_2(z) , ···, a_k(z) be analytic in D such that a(z) not≡ 0. If f(z) ≠ 0 and the zeros of f~((k)) (z) + a_1(z)f~((k-1)) (z) + ··· + a_k(z)f(z) - a(z) are of multiplicity at least 2 for each f ∈ F, then F is normal in D. This result improves Miranda' s normal criterion.