scholarly journals Normal Families concerning Polynomials and Shared Values

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Xin-Li Wang ◽  
Ning Cui
Keyword(s):  
Positive Integer ◽  
Meromorphic Functions ◽  
Shared Values ◽  
Normal Families

We study the problem of normal families of meromorphic functions concerning polynomials and shared values. We prove that a family ℱ of meromorphic functions in a domain D is normal if, for each function f∈ℱ, Pfzfkz=a⇔fkz=b, where P is a polynomial with the origin as zero, k is a positive integer, and a ≠0, b are two finite constants.

Normal families of meromorphic functions concerning shared values

2013 ◽  
Vol 58 (1) ◽  
pp. 113-121 ◽  
Author(s):  
Jian-Jun Ding ◽  
Li-Wei Ding ◽  
Wen-Jun Yuan
Keyword(s):  
Meromorphic Functions ◽  
Shared Values ◽  
Normal Families

Normal families of meromorphic functions with shared values

2016 ◽  
Vol 36 (1) ◽  
pp. 87-93 ◽  
Author(s):  
Wei CHEN ◽  
Honggen TIAN ◽  
Peichu HU
Keyword(s):  
Meromorphic Functions ◽  
Shared Values ◽  
Normal Families

Exceptional functions and normal families of holomorphic functions with multiple zeros

2011 ◽  
Vol 18 (1) ◽  
pp. 31-38
Author(s):  
Jun-Fan Chen
Keyword(s):  
Positive Integer ◽  
Meromorphic Functions ◽  
Normal Family ◽  
Holomorphic Functions ◽  
Normal Families ◽  
Multiple Zeros ◽  
Zeros Of Functions

Abstract Let k be a positive integer, and let ℱ be a family of functions holomorphic on a domain D in C, all of whose zeros are of multiplicity at least k + 1. Let h be a function meromorphic on D, h ≢ 0, ∞. Suppose that for each ƒ ∈ ℱ, ƒ(k)(z) ≠ h(z) for z ∈ D. Then ℱ is a normal family on D. The condition that the zeros of functions in ℱ are of multiplicity at least k + 1 cannot be weakened, and the corresponding result for families of meromorphic functions is no longer true.

Normality and shared values concerning differential polynomial

2011 ◽  
Vol 18 (2) ◽  
pp. 299-306
Author(s):  
Chunlin L. Lei ◽  
Degui G. Yang ◽  
Cuiping P. Zeng
Keyword(s):  
Positive Integer ◽  
Meromorphic Functions ◽  
Differential Polynomial ◽  
Shared Values ◽  
Complex Numbers

Abstract Let ℱ be a family of meromorphic functions in a domain D; let k ≥ 2 be a positive integer; and let a, b and c be complex numbers such that b ≠ 0 and a ≠ c. If, for each ƒ ∈ ℱ, all zeros of ƒ have multiplicity at least k, ƒ(z) = a ⇔ D(ƒ) = b, and D(ƒ) = 0 ⇒ ƒ(z) = c, where D(ƒ) is the differential polynomial of ƒ(z), then ℱ is normal in D.

Normal families of meromorphic functions and shared values

2010 ◽  
Vol 165 (3-4) ◽  
pp. 569-578 ◽  
Author(s):  
Xiangzhong Wu ◽  
Yan Xu
Keyword(s):  
Meromorphic Functions ◽  
Shared Values ◽  
Normal Families
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