PROOF OF HAYMAN'S CONJECTURE ON NORMAL FAMILIES

Abstract

In 1964, Hayman posed the following conjecture. Let a(≠0) and b be two finite complex numbers and suppose n(≥5) be a positive integer. If is a family of meromorphic functions in a domain D and for each f∈ and z∈D, there exists f'(z)—af(z) n ≠b, then is normal in D. This paper aims at giving a proof of the conjecture.