(untitled) (Communications in Mathematical Research, 2021)
In this paper, we consider normality criteria for a family of meromorphic functions concerning shared values. Let F be a family of meromorphic functions defined in a domain D, m, n, k and d be four positive integers satisfying m ≥ n + 2 and d ≥ k + 1m − n − 1, and a(≠0), b be two finite constants. Suppose that every f ∈ F has all its zeros and poles of multiplicity at least k and d, respectively. If (f^n)^(k)−af^m and (g^n)^(k)−ag^m share the value b for every pair of functions (f, g) of F, then F is normal in D. Our results improve the related theorems of Schwick (Schwick W. Normality criteria for families of meromorphic function. J. Anal. Math., 1989, 52: 241–289), Li and Gu (Li Y T, Gu Y X. On normal families of meromorphic functions. J. Math. Anal. Appl., 2009, 354: 421–425).