Normal Family of Meromorphic Functions

Abstract

Abstract. We study normality for families of meromorphic functions which is related to an extended version of a Hayman's conjecture on value distribution, and prove several normality criteria for meromorphic functions and certain non-homogeneous differential polynomials.

Quasi-normality and Shared Functions

“…The following example illustrates Theorem 2.6. In 1999, Fang and Hong extended Montel's normality test using the concept of shared set [5]. They proposed the following Theorem.…”

“…Theorem 2.8 ( [5]). Let F be a family of functions meromorphic on a domain D. If each pair f and g in F shares the set S = {0, 1, ∞} then F is normal on D.…”

Normality of meromorphic functions and differential polynomials share values

“…All authors read and approved the final manuscript. 1 School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China. 2 Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou, 510006, China.…”