The value distribution of fm + a(f(k))n and normal families of meromorphic functions

Abstract

In this paper, we obtain a normal criterion of meromorphic functions concerning shared values. Let Dbe a domain in C and F be a family of meromorphic functions in D. Let k, n,m ∈ N+, n ≥ mk+m+1, and a, btwo finite complex numbers with a 6= 0. Suppose that every f ∈ F has all its zeros of multiplicity at least k + 1 . If fm + a(f(k))n and gm + a(g(k))nshare the value b IM for every pair of functions (f, g) of F, then F is a normal family in D.