Some normality criteria for families of meromorphic functions
نویسندگان
چکیده
*Correspondence: [email protected] 4School of Economic and Management, Guangzhou University of Chinese Medicine, Guangzhou, 510006, People’s Republic of China Full list of author information is available at the end of the article Abstract In the note, we study the normality of families of meromorphic functions. We consider whether a family of meromorphic functions F is normal in D if, for a normal family G and for each function f ∈F , there exists g ∈ G such that f nf ′ = ai implies gng′ = ai for two distinct nonzero points ai , i = 1, 2 and an integer n. An example shows that the condition in our results is best possible. MSC: Primary 30D45; secondary 30D35
منابع مشابه
Some Normal Criteria for Families of Meromorphic Functions
In the paper, we study the normality of families of meromorphic functions related a Hayman Conjecture. We consider whether a family meromorphic functions F is normal in D, if for each function f in F , f ′ + af = b has at most one zero, where n is a positive integer, a and b = 0 are two finite complex numbers. Some examples show that the conditions in our results are best possible.
متن کاملNormal Criteria of Function Families Related to a Result of Drasin
We study the normality of families of meromorphic functions related to a result of Drasin. We consider whether a family meromorphic functions F whose each function does not take zero is normal in D, if for every pair of functions f and g in F, f z and g z share ∞ or H f − 1 and H g − 1 share 0, whereH f : f k z ak−1f k−1 z · · · , a0f z . Some examples show that the conditions in our results ar...
متن کاملSome normality criteria of functions related a Hayman conjecture
* Correspondence: [email protected]; [email protected] School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China School of Economic and Management, Guangzhou University of Chinese Medicine, Guangzhou 510006, China Full list of author information is available at the end of the article Abstract In the article, we study the normality of families of meromorphic ...
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 کاملSome Normality Criteria of Meromorphic Functions
Let f be a nonconstant meromorphic function in the complex plane C. We shall use the standard notations in Nevanlinna’s value distribution theory of meromorphic functions such as T r, f , N r, f , and m r, f see, e.g., 1, 2 . The notation S r, f is defined to be any quantity satisfying S r, f o T r, f as r → ∞ possibly outside a set of E of finite linear measure. Let F be a family of meromorphi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013