Normal families and value distribution in connection with composite functions
نویسندگان
چکیده
منابع مشابه
Normal families and value distribution in connection with composite functions
We prove a value distribution result which has several interesting corollaries. Let k ∈ N, let α ∈ C and let f be a transcendental entire function with order less than 1/2. Then for every nonconstant entire function g, we have that (f ◦ g) −α has infinitely many zeros. This result also holds when k = 1, for every transcendental entire function g. We also prove the following result for normal fa...
متن کاملComposite Holomorphic Functions and Normal Families
and Applied Analysis 3 Remark 1.5. In Theorem 1.2 setting α z constant zero and P z,w a polynomial in variable w that vanishes exactly on a finite set of holomorphic functions S, we obtain Corollary 1.6 which generalizes the famous Montel’s criterion that a holomorphic family omitting 2 or more values is normal. Corollary 1.6. Let F be a family of holomorphic functions on a domain D. Let S be a...
متن کاملFixed Points of Composite Meromorphic Functions and Normal Families
We show that there exists a function f meromorphic in the plane C such that the family of all functions g holomorphic in the unit disk D for which f ◦ g has no fixed point in D is not normal. This answers a question of Hinchliffe who had shown that this family is normal if Ĉ\f(C) does not consist of exactly one point in D. We also investigate the normality of the family of all holomorphic funct...
متن کاملThe value distribution of f + a(f ) and normal families of meromorphic functions
In this paper, we obtain a normal criterion of meromorphic functions concerning shared values. Let D be a domain in C and F be a family of meromorphic functions in D. Let k, n,m ∈ N, n ≥ mk+m+1, and a, b two finite complex numbers with a 6= 0. Suppose that every f ∈ F has all its zeros of multiplicity at least k+ 1 . If f + a(f ) and g + a(g)share the value b IM for every pair of functions (f, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2005
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2005.03.045