Some normality criteria of meromorphic functions

Some normality criteria of functions related a Hayman conjecture

“…In this area, Schwick [7] first proved an interesting result that a family of meromorphic functions in a domain is normal if in which every function shares three distinct finite complex numbers with its first derivative. And later, more results about normality criteria concerning shared values have emerged, for instance, (see [8][9][10]). In recent years, this subject has attracted the attention of many researchers worldwide.…”

“…Zhang [10] gave the following example to show that Theorem 1.4 is not true when n = 1, and therefore the condition n ≥ 1 is best possible. Here f # (ξ) denotes the spherical derivative…”

“…In 2008, Zhang [10] obtained a criterion for normality of F in terms of the multiplicities of the zeros and poles of the functions in F and use it to improve Theorem 1.2 as follows. Theorem 1.3 Let F be a family of meromorphic functions in D satisfying that all zeros and poles of f ∈ F have multiplicities at least 3.…”

Normality and shared values concerning differential polynomials

“…In 2004, Fang and Zalcman [5] proved Recently, Zhang [13] proved Theorem B. Let F be a family of functions meromorphic in a domain D, let n 2 be a positive integer, and let b be a finite complex number.…”

Normal families of meromorphic functions sharing values or functions

“…In 2008, Q. C. Zhang [8] proved the following Theorems C and D, which generalized the condition f (k) ≠ 1 in Theorem A to shared value when k = 1 and generalized Theorem B when n ≥ 2, respectively. Theorem C. Let F be a family of meromorphic functions in D satisfying that all of zeros and poles of f ∈ F have multiplicities at least 3.…”