We studied the normality conditions in families of meromorphic functions, improved the results of Fang and Zalcman [Fang ML, Zalcman L, Normal families and shared values of meromorphic functions, Computational Methods...We studied the normality conditions in families of meromorphic functions, improved the results of Fang and Zalcman [Fang ML, Zalcman L, Normal families and shared values of meromorphic functions, Computational Methods and Function Theory, 2001, 1 (1): 289-299], and generalized two new normality criterions. Let F be a family of meromorphic functions in a domain D, a a non-zero finite complex number, B a positive real number, and k and m two positive integers satisfying m〉2k+4. If every function denoted by f belonging to F has only zeros with multiplicity at least k and satisfies f^m(z)f^(k)(Z)=α→ |^f(k)(z)| ≤B or f^m(z)f^(k)(z)=α→|f(z)| ≥, then F is normal in D.展开更多
文摘We studied the normality conditions in families of meromorphic functions, improved the results of Fang and Zalcman [Fang ML, Zalcman L, Normal families and shared values of meromorphic functions, Computational Methods and Function Theory, 2001, 1 (1): 289-299], and generalized two new normality criterions. Let F be a family of meromorphic functions in a domain D, a a non-zero finite complex number, B a positive real number, and k and m two positive integers satisfying m〉2k+4. If every function denoted by f belonging to F has only zeros with multiplicity at least k and satisfies f^m(z)f^(k)(Z)=α→ |^f(k)(z)| ≤B or f^m(z)f^(k)(z)=α→|f(z)| ≥, then F is normal in D.