Normality criteria of meromorphic functions for dierential monomial sharing a holomorphic function - Sun, Cheng-Xiong (Journal of Global Research in Mathematical Archives(JGRMA), 2014)
Itis mainly proved: let k be a positive integer, and m be an even number. Suppose that a(z)(6 0) is a holomorphic function with zeros of mul-tiplicity m in a domain D. Let F be a family of meromorphic functions in a domain D such that each f 2 F have zeros of multiplicity at least k + 1 + m and poles of multiplicity at least m + 1. For each pair (f; g) 2 F, if ff(k) and gg(k) share a(z) IM, then F is normal in D. Key words: Meromorphic functions; Holomorphic functions; Normal family;Sharing holomorphic function.